if by traditional books you mean las vegas the differences are:
1) you can get reduced juice offshore
2) you can get a bonus on your initial deposit offshore
3) if you have a good book, you can bet a much larger variety of props and other bets.
4) and obviously, with an offshore book, you can bet from you computer or by phone rather than being there in person. of course, your account needs to be funded with your own cash.
the main thing you should look for, in my opinion, is safety. second thing is reduced juice. third thing is bonus.
you probably want to open accounts at at least two books so you can shop for the best line. might i suggest pinnacle and hollywood to start?
good luck