I've not had any similar problem with the stock browser. I've just had a browse to facebook (normally use the app) and it was fine.
Do you have a lot of windows open at once ? I always try and close ones I'm done-with down. I also always close the browser once I'm finished (delete all the windows, open a new one and then hit Back) since on Android it will keep running and if you're on a page with re-loading ads (for example) they will continue to load even while you're not looking at it.
iPhones simply stop apps you're not looking at (unless they're specifically written to carry-on and even then they do so in a very limited way)..