It's everything! Your not those guys so don't expect to be able to emulate them without a lot of work(Depending on how far away you are from them).
Now, if you don't mind things like "Hey, that was an awesome solo! It reminded me of Steve Gaines" said to you every night you perform then...
Learn all his solos inside and out. Analyze what he is doing(try to figure out why he did what he did). "Steal" his ideas by playing them with slight modifications/variations to make them your own(not the whole solo but fragments of it).
It's all about practice though. Just sit down and play with those guys over and over and over. Eventually you'll start to hear things that they do such as how they bend and release, vibrato, slide, etc...
What makes guitarists different is the how they choice the notes in the solo and how they phrase them. Since you are starting by copying the notes you have to learn how to phrase it like them.
It is analogous to trying to copy an accent. You can learn the "words" relatively easy but what is hard is the accent which is the "phrasing". No matter how many "words" you know, you won't sound authentic until you get the accent down. Once you get the accent down you can then learn the words as you like. The "accent" tends to be the hardest for most people.
There is also a stylistic aspect you should have. If your going to play country you gotta have a fiddle in the band! Oops, I mean, you gonna play in Texas... damn, I mean you gotta have some experience with it.
So go practice their solo's over and over and over then start trying to incorporate their ideas into yours. Make sure you can do a lot more than just their solo's though. You need to be able to solo over a country progression too(you can copy the songs to start), etc...
Just go for it dude! It's really simple but just hard work! It will take you months, if not years to get it down pat.
BTW, just so you know, what I mean by analyzing is to look at the solo's and try and figure out what they did over chord X. What notes did they use over that chord, with respect to it, and how? Did they bend from the 2nd to the 3rd or the 3rd to the 4th? All guitarists have key things they do that make them who they are.
Ok, here is a clip of me trying to imitate the sound and phrasing of a guy I liked -
I wrote up a long description of what the differences were and such but instead of posting it now I'll ask you what you hear. That clip was my "tone quest" a few years ago when trying to understand why what I played sounded dead and why what he played sounded so good. I was given all kinds of answers through the years mostly from people that didn't have a clue and hence gave the most "obvious" answer(to anyone that didn't have a clue).
When I hear the two licks back to back I hear a huge difference. I can hear a difference in phrasing but IMO it's surprisingly close(of course I spend a lot of time trying to play just like him). But I now know the real difference that's going on and why(it's quite obvious now but wasn't back when I was trying to understand it).
Now, the differences may not be a big deal to most people but to me, when trying to sound just like him mine version is obviously off(it sounds lifeless to me). Maybe it's just in my imagination but there is objective differences. Phrasing has little to do with it.
Anyways, you can see both visually and aurally the differences... can you tell me what they are? In any case this is more of an example of how I worked on my quest to emulate the tone of someone else(not necessarily the style).
If you post some clips of an "A/B" comparison then we can discuss the differences and someone might know exactly what the problem is(similarly someone might know exactly the problem with my clip... although I think I already know the answer I could be wrong).