Hmm. Same thing. Got to tune them no matter it's double pedals or two singles. Troublesome!
Two single pedals and double pedals are very different.
No matter what kind of double pedal you're using - strap drive, direct drive, or chain drive, the slave pedal will feel slightly off due to the friction, and the fact that a lot of energy is lost thru the transmission from pedal -> shaft -> beater. that's why even if both your legs are well trained, your left pedal will still feel different, but of course thru training and time you'll be used to it, and it won't pose much of a problem.
For dual bass drums, you're playing on two single pedals, which means two pedals with identical feels, assuming spring tension and beater distance are all equal. Some people like it this way, because the feel is the same for both pedals.
Drawbacks for dual bass drums are mainly space contraints - its a bitch to have 2x bass drums sitting around, and tuning will be a bitch too.
But the good thing about having 2 bass drums is that you can have two bass drums of different sizes, ie. 18" and 22", thus effectively having two different sounds when you kick. some people love it, some people hate it, its all personal preference.
Pros for double pedal are mainly cost and convenience - a pair of double pedals are definitely cheaper than dual bass drums, and you can pack them into a carrying case for a gig (how many gigs give you TWO bass drums?!)