I found that Chrome destabilized and black-screened a lot when I had 1500+ tabs open, but Opera oddly enough did not. Opera seems to have slightly better memory management and background tab handling. (Puts them to sleep better.) That said, it does still take a very long time to reopen that many tabs. That's where stability comes in... you don't want to have to close and reopen your web browser throughout the day, if you can avoid it.

Opera does indeed have switch to tab, FYI - and open tab searching.