If you like both equally, go for Elizabeth - it's the ultimate classic name, could suit anyone, and gives her the widest choice of nicknames if she wants one or doesn't like the full name as she grows older.
Isabel is very pretty (the original spelling, I think Isabelle looks overdone unless you have French heritage). The major problem with this name apart from popularity is the variety of spellings (there's also Isobel, as well as all the Isabella's). She would often be correcting people I think.