Actually they're quite different. I've studied portuguese under Brazilian teachers and under one Portuguese teacher from Coimbra.
Portuguese from Portugal sounds vastly different from Brazilian Portuguese. It might as well be a different language altogether. People from Portugal have no problem understanding Brazilians, however, most Brazilians have a very difficult time understanding the Portuguese. For that reason most Portuguese movies are dubbed in Brazil--it's that different.
Portuguese from Lisbon sounds more slavic than like any other romantic language IMO. When I first watched a news clips from Lisbon the difference in pronunciation was astounding. I find the accent from Coimbra tolerable and much softer. Personally I can't stand the Lisboa accent.
Also, like in most languages words mean different things in both countries. For instance, "rapariga" means "girl" in Portugal. In Brazil, it means "bitch". While in Brazil, one of my portuguese friends found that out the hard way. I've studied Brazilian portuguese for over a year yet when I'm around a group of Portuguese I still find them nearly unintelligible. People from Mozambique and Angola are easier to understand and IMO is a little closer to the Brazilian Portuguese I'm used to.
All that aside the differences in pronunciation between "Brazilian" and Portuguese from Portugal is far different from any differences I've ever encountered between Anglophone or Hispanophone countries.