I recently moved from Hyperion to Balmung recently to meet up with real life friends, and both servers were/are good to me. Can't go wrong with either, in my opinion. Here's my take on the differences I've seen first hand between the two:
1. Hyperion is definitely lower population relative to Balmung, although it's not low population. I.e. It's not empty feeling at all, but you won't see the crowds that Balmung has going on, particularly in starting cities.
2. Balmung really is a RP server. It's like night and day between the servers. You can't go 2 steps on Balmung without coming across someone RP-ing in a main city, and it's not uncommon at all to find people out in the middle of nowhere doing it too. I kind of like the atmosphere of it even though I don't participate, and there's no requirement at all to participate. I can't ever recall seeing much public rp on Hyperion at all, although I'm sure there's some dedicated FCs that do it regularly.
3. Even though they're both Legacy servers, Hyperion feels much more saturated in that legacy atmosphere. You'll find more players who are legacy than on Balmung for example, possibly due to Balmung's rp making it more likely for newer characters being played more often for rp purposes.
4. Certain status quo ways of dealing with mechanics are different since they're on different data centres. The most obvious example is The Labyrinth of the Ancients' Bone Dragon fight. Hyperion's data centre uses the fight at the north edge strategy, whereas Balmung's data centre uses the fight in the middle strategy. There are other examples here and there, so be prepared to adjust your tactics for a few fights here and there if switching data centres.
P.S. It's not too difficult to find a time when Balmung is available to create a new character on if you decide you want to go that route. You won't be able to do it during prime time, obviously, but it's not as extreme as needing to wait until 4 in the morning to do it either thankfully. You can always dabble around with starting storylines to see what they're about on one server until you are able to find a time to create one on a high population server as well.