You should almost certainly use Facebook Connect as your only signup option - all the data I've been privy to shows that the improvements in engagement more than make up for lost signups.
I'll put you on my list of "people I will never do business with on principle", but if I'm your target market then you've got much bigger problems than that.
I wonder (and I'm speculating, because I haven't seen the data you refer to) whether there's a bit of selection bias here: the people who are likely to log in via Facebook are already more likely to 'engage' (if I were being rude, I'd say 'click on any old crap and spam their friends) than those who aren't, so it's only a proportional increase in engagement, not an absolute one.
I'll put you on my list of "people I will never do business with on principle", but if I'm your target market then you've got much bigger problems than that.