Hey and welcome to TOG.
We don't really have a main focus, other than playing the game. There are people interested in all aspects of the game, so we're pretty generalist. We're currently in the process of trying to figure out our active numbers, since GW2 doesn't have very good guild management tools, unfortunately, but at least check EU was split about 50/50 across the two servers.
There are events in the EU timeslots for both servers, and you can check that out in the Events subforum in our GW2 forum. Most of the events are in the forms of dungeon runs, it seems, but we gathered up for the Lost Shores events and had a great time on TeamSpeak, for example, and have done similar things for the Halloween events. Other than that, anyone is free to organize events, so if you see something missing, you could always step up and run it yourself.
Perhaps a good start would be to check the Events forum and see if there's anything interesting there in your timezone and try that server first. While there is a cooldown of a week, the transfers are still free, so if you feel that the server you chose is too quiet, try the other. Both Desolation and Yak's Bend EU are in the same guild, so we're always chatting with each other anyway.