100% this has something to do with the internet connection.
Whenever I'm online in-game, I go to the XMB to check out who's online, my trophies and other things. Usually, the friends list loads up quickly and stuff, but lately, it loads up slow, including the avatars and trophy info, reading messages and every other information that shows up when online.
To top it all off, when I go back to the game, it literally takes 3-5 minutes. It gets stuck where the XMB disappears, but the dim screen with the clock thingy on the upper right hand stays.
This only happens when I'm signed in, which can also take forever.
The funniest part is when I get in a game, there's no lag at all. I don't even have trouble finding games on matchmaking games.
Then I test the internet connection on Network Settings, and it says my download speed is 11+ mbps. I go download from the Store, I get 100 kbps.
I already tried rebuilding the database and it didn't work. I'd appreciate it if someone knows how to get around this. It's really annoying having to message someone and take 10 minutes to do it.
Online games actually transfer very small packets of data, so they don't require much bandwidth. As long as the latency of the connection is reasonably low, you won't have any problems playing online, even if your downloads are slow. The XMB will generally be less responsive when a game is running, because the XMB has less system memory available to it when it is running during a game. How much slower will depend on the performance of the Internet connection. The XMB has to download data more often when it is running during a game, than it does when it is running by itself.