Well, I've primarily raided in 10 man, but did 25's at the start of T-11 and for the 2nd and 3rd weeks of DS on my shammy (even got a couple top 5-percentile parses on her). So, it's hard to say how much of the transition is due to raid size, and how much of it is from raiding on a different class. I agree that strict healing assignments are more common in 25's, and that it feels like healing is more teamwork-oriented. You have to be more aware of incoming heals, it can be a little frustrating setting up a big heal and it all goes to overheals, since someone else had a little more haste.
Compared to FL and T-11, there's far more raid stacking, so you don't usually have to be as cautious about who you heal with PoM or other spells that bounce from one player to another, but that's true of both raid sizes. In FL and T-11, it made a much bigger difference for 10's vs. 25's. For disc (I play it primarily with holy OS on some fights, or if we need another priest to go disc), I can bubble-spam more effectively in 10's than I can in 25's - there's no way to get shields on everyone (I'd run out of mana, and the ones I put on first would run out before I finished). So, I watch and see who tends to take more damage, and try to get my pre-casts and bubbles on them first.
Vent (or Mumble, or whatever voice chat you use) may have a very different tone/feel than you're used to. If multiple people are calling things in 25's it can be very chaotic, even more so than on 10's.