So ignoring the pet hating sociopaths for a minute, here's my breakdown --
Dog pros --
more likely to be a "social" companion
more easily trained
if trained, less likely to destroy furniture
great wingman if you're single
Dog cons --
You have to get it exercise. If you're in an apartment, that means walking it. And it means walking it regardless of the weather. That sounds good until it's -5 and windy.
You can't leave it home all day.
Pet dander in the house is worse.
Simply more expensive to own
If you have hardwood floors, prepare to deal with them being scratched.
Cat pros --
Lower maintenance
Generally calmer once they reach adulthood
You can (and should) get more than one -- two dogs is a lot for most people
Easier to clean up after (that includes vomit, by the way. Medium-sized dog puke is pretty much like a toddler vomiting in their bed. Cat puke is much more manageable, though they do throw up more often)
Cat cons --
Less "social" in the sense that they're not waiting at your door to greet you and jump in your arms when you come home. Greater chance (probably 30%) that he/she will just want to be left alone. But most cats are still very affectionate.
They will claw your furniture to he!!. There's nothing you can do about it.
More of your visitors will be allergic (at least that's my experience).
