I noticed on my lower end Windows phone that the UI did lag, but that was likely because it didn't even have 1GB of RAM. And then I went from that to a 2GB device and the problem didn't completely go away because of animations. But at least they weren't laggy animations? Also, I have noticed that there is sometimes a slight animation issue when you are trying to go to your home screen if you have no available RAM... or at least it happens to me at times. To me, like I said, it's all about having RAM for applications. Imagine a phone where the processor is fast enough, the RAM is plentiful enough, and you can hold those three applications back without refresh.
Not to bash a single phone, but I have a 1GB RAM phone and it sometimes opens things slower than my 3GB RAM phone. This is normally on second opening, obviously.