There are many differences between boosting and cutting with EQ. I'll discuss the ones that stand out to me the most:
One way to think about a mix is that it's like packing a box, or perhaps like playing Tetris. You're trying to get all these things to both fit together and also fit into a limited space. With a mix, you've got your dynamic range and your frequency response and that kinda makes a box that everything has to fit into. For many mixes, you not only want to make sure everything fits in the box, you also want the box to be mostly full, or at least not mostly empty, and you want some of the things in the box to be bigger or smaller or a certain shape. Like Tetris, you are usually given certain shapes to work with and you have to figure out how to make them fit. Sometimes you can get some control over what you're given to mix, but not always.
To me, EQ is like a way to change the shapes that you're given while you're packing them into the mix. So that's pretty cool! Imagine being able to do that in Tetris! To abuse the Tetris analogy, cutting EQ might be like taking little squares off of a Tetris shape, while boosting is like adding little squares. Hopefully that analogy alone starts you thinking about why boosting can be trickier.
When you boost, you're giving yourself more stuff to try to fit into the same total space, while cutting actually makes it a bit easier to fit it all in. Now you can't just cut for free without consequences. First off, you usually don't want the shapes you were given to be completely carved away to nothing, and you also want to have the box more or less full when you're done, but judicious cutting more often makes things easier and not harder. Reckless boosting can make the mix a lot harder.
Another aspect of cutting that is easier is that if you cut something bad, then there's less bad in the mix, and maybe you cut little bit of something good accidentally at the same time, but it's not too hard to tweak the EQ to retain as much of the good as possible when you're cutting. But when you boost, you can be adding both good and bad, and tweaking a boost to only boost the good and not the bad is harder. The bad stuff brought out by an EQ boost sticks out like a sore thumb. The good stuff cut away by an EQ cut many times won't be missed.
Cuts also depend less on what you're given. When you cut, you're throwing away something you don't want. If what you're cutting wasn't there in the first place, then it doesn't hurt anything to cut it anyway. Boosts don't work at all if there's nothing there to boost. EQ cannot create frequencies, it can only multiply them. 1000 times 0 is still 0. So if you have a recording of a soprano singer and you try to boost something like 50 Hz, you're just going to be adding noise. That's an extreme and ridiculous example, but many engineers don't realize when they don't actually have the frequencies they are trying to boost. So when boosting, you have to be carefully listening and hearing what you've got and how you're changing it. There are a lot of cuts you can make blind (or maybe I should say "deaf"), like you can high pass 80 Hz and up on most tracks without even thinking about it and not mess up a mix.
That brings up another difference: If you cut the same frequencies on several tracks, they are basically all getting out of each other's way. But if you boost the same frequency on several tracks, they will start to fight each other. So you have to remember or keep track of your boosts and make sure you don't overlap too many of them. Cuts you can make and then forget about without having to figure out in the future why the 1000 - 1200 Hz range sounds so busy (for example).
Finally, I want to pass along some advice I read online many years ago: Use cuts to make a track sound better, use boosts to make it sound different. Thinking about that advice, it also show why cuts are easier. Taking away the bad is pretty straightforward, because you know what you're trying to take away before you take it away. It's like opening a fridge and getting rid of only the bad cheese: just look for the moldy ones and throw them away. Now imagine the same fridge filled with 30 unlabeled cheeses and you're not sure which one will go best with the bottle of wine you just opened and you can see why boosting is harder: You have to find the best boost(s) through trial and error. You basically have to taste a little of every cheese before you know, unless you have a lot of experience with all kinds of cheeses. If you're boosting to make it sound different, it's not alway obvious which differences will sound better and which will sound worse.
Hopefully that gives you some ideas about why it's different to boost versus cut. I could type a lot more if I had the time. But instead of my typing and you reading, we should both be mixing/producing. The more you work with EQ, the more these things will become apparent to you. The hard truth about mixing is that you can't really learn more than 5% of it by reading the web. You have to go do it.
I've started to think there's an aspect of this question that hasn't been fully addressed yet:
So, isn't it just the shape of the EQ curve that matters? It seems to me that whether more or less of it is above or below the 0dB line shouldn't matter, because I'm going to adjust the overall track volume anyway, to achieve the mix that I want.
Thinking about the quote above, I think what's going on here is maybe you're conflating the science of how EQ and filters work with the art of mixing.
For starters, the EQ curve that you create with your EQ settings is not determining the time-average power levels of the frequencies the track. All that EQ does is change the time-average power levels of the frequencies the track. The raw recording has the most impact on the final time-average power levels, and almost every other process you might do on a track (plugin or effect) also changes the time-average power levels of the frequencies of the track. So the final result of what you get in the mix for a track is like 80% - 90% based on the recorded sound, maybe 5% - 8% based on the EQ settings, and then the rest is the smaller effects of compression, modulation effects (chorus, flange, phase, etc.) and so on.
So EQ is a really small part of your mix, and the sound of the track itself is much more powerful than the EQ of the track in terms of what it does to a mix.
Going back to the line drawn by the EQ settings, you have to overlay that line on top of the power spectrum of the track and then you can get a slight idea of how the track is contributing different frequencies to the mix. Like if you cut or boost everything below 150 Hz on a track of a soprano vocalist, well you just did almost nothing to the sound of the mix because there wasn't anything there to cut or boost!
And you would be surprised at how many frequency ranges in most tracks pretty much cannot be boosted because there's just nothing there. Depending on how it's tuned and played and miked, you can have a kick drum track where boosting 900 Hz by 18 dB does pretty much nothing but add noise. And that's just one obvious example.
The other thing I want to address is don't mix with your eyes, don't mix with a calculator or with science, mix with your ears. The line on the EQ curve can't tell you whether a track is going to sit right, only your ears can do that. Ears are much more sensitive and effective and discerning than any meter, analyzer, or other device or scientific data. Boosting is harder than cutting because of the way the sound of the mix changes when you boost versus when you cut. It has nothing to do with overall gain of the track or anything besides that.
Not only is it not just the shape of the EQ curve that matters, the shape of the EQ curve doesn't matter at all! I can't emphasize that enough but I don't want to go all caps. The shape of the EQ curve is immaterial. The only things that matter are how the track sounds and how the mix sounds, and the shape of the EQ cannot tell you either of those things.
Let me go back to Tetris one more time to address the part about EQ versus overall gain. EQ is like adding or removing little squares from a Tetris shape. Overall gain is like making the whole shape bigger or smaller. So which is easier to deal with in Tetris, a really huge square (all squares but one were taken away with subtractive EQ and then overall gain was boosted a lot), or a small crazy shape with little squares and lines sticking out all over (a bunch of different boosts adding squares to the original shape in random places and then the gain brought down a lot)? Subtractive EQ makes tracks easier to mix because it makes them into "smaller, simpler shapes". Then you can scale those simple shapes up and down to make them the right size and they are easy to pack together. Additive EQ makes larger, more complicated shapes. Shrinking the whole thing down after boosting some frequencies doesn't make the shape any better, just smaller. And if you boost enough and then drop the gain to make it fit in the mix, you just end up with something that sounds terrible and quiet, when what we want is good and loud.
Even though I already put in at least 1,000 words, I thought a picture might help:
Notice how when EQ is boosted, it can be harder to get the EQ right, and the consequences of getting it wrong are worse for the mix than getting it wrong with cutting. Yes, I know that the shape scaling isn't exactly "fair", but the way actual audio works is more like this.