I agree with Turion's answer. I would add a few additional points:
I found that when I went to play the pieces I had learned on an acoustic Yamaha upright, I had extreme difficulty getting the instrument to sound soft and melodic
Acoustic Yamaha upright pianos are notably (or notoriously, depending on who you ask) "bright". That is, they consistently have a bell-like, piercing tone to them rather than a more soft, mellow, rounded sound. So first off, I would say that your experience probably has much to do with the sound itself.
Are grand pianos "heavier"? Is it easier to play notes softly on them?
Generally, yes and yes. A couple things come to mind.
I would note that if you are accustomed to using the "soft pedal" to assist playing very quietly, you should be aware that the soft pedal action on a grand is completely different than the soft pedal action on an upright. An upright assists your playing softly by moving the hammer fallback rail closer to the strings, so that less of the force applied by the key to the action actually translates into hammer velocity.
By contrast, the soft pedal on a grand actually moves the entire action slightly to the right which has two effects on the tone. First, the notes where the hammers strike two or three strings normally now only strike one or two strings, thereby producing less sound. (The remaining not-struck strings are of course still free to vibrate sympathetically.) This of course explains why the soft pedal on a grand is called the una corda -- the "one string" pedal. Second, hammers are made of felt which gradually gets grooved as it repeatedly strikes the strings. Hitting the soft pedal changes the intersection of the hammer head and the strings such that the ungrooved portion of the felt strikes the strings. This typically produces a more dull tone.
Leaving the soft pedal aside, there are also big differences in the grand action compared to the vertical action. The different mechanical advantage of a longer key was already mentioned. An obvious difference is that the hammer is being propelled upwards, against gravity, instead of sideways in a vertical action, which certainly has an effect upon how well you can control the velocity with which the hammer strikes the string. Grand actions also have an additional escapement which vertical actions lack, which allows for faster repetition at a given volume.
Are uprights and grand pianos different enough that certain styles of music prefer one or the other?
It's complicated. Obviously if you know a particular piano well then you'll be a lot better at playing any piece in any style on it, and you'll be a lot better at knowing what sorts of pieces sound best on that piano. There are some pianos that call out to have ragtime played on them, and those are maybe not the best pianos for Rachmaninoff, and vice versa.
You'll also find as you play more pianos that different manufacturers make pianos with different characteristics. Every Yamaha upright I've ever played had exactly the same bright tone and crisp touch. Yamaha approaches piano building as an engineering discipline; everything from the way they cast the iron plates to the assembly of the action parts is tightly controlled to narrow tolerances. Steinway by contrast builds pianos of extremely high quality but with a great deal more variation in them; two Steinways of the same model can come out of the same factory and have quite different tones to them.