I haven't owned either species, but I have worked with them. Quakers are much more outgoing and better talkers and can be super snuggly. Senegals can be super snuggly as well and very laid back, they also have a tendency towards being quiet. Both can be nippy, quakers are known for being cage possessive and senegals are known for being phobic :shrug:
The biggest difference to me is the outgoing, bossy nature of the quaker versus the shy, more timid nature of the senegal. Both make amazing birds and wonderful pets, and both go through a rather nippy hormonal stage around 1-2 years of age, and both tend towards being one person birds. Once you pass that nippy stage, and you handle it properly, they do great! And if you socialize them well they will go to anyone :wink: That's the hardest part to me!
They can definitely be noisy little so-and-so's when they want to be, Keiko (Quaker) used to be a real nice screamer, it was ear piercing. They need plenty of interaction, toys, a play gym and anything that will keep them busy, otherwise, you will likely come across a screamer.
They are very cuddly, well my Quaker is. I have had problems with Keiko, only in the past, he attacked my face at any chance he got, but with a lot of work and patience, we got past that and he's been an angel ever since. He is an excellent talker, says 20+ words and he's always willing to hang out with you while you're watching TV, on the Computer etc etc. Keiko's pretty much stuck to me like glue, but I've taught him to play independently, he is bonded to me, but he will let someone pet/scritch/hold him occasionally, usually if he's on me, no one is aloud to touch him though.
I guess this also depends if you were to get a rescue, rehome or hand-raised Quaker too. If you get a hand-raised Quaker, you have the chance to get it while it's young and socialize it with more than one person in order to have it bond with everyone and not just one person. (unless you don't mind it only bonding to you)
Overall, I think they're fantastic birds, they do go through phases/hormonal stages like all birds, but it's something you have to work with and be understanding of. I don't know anything about Senegals, but I have heard nothing but good things about them.
I have a Sennie & have had a Quaker, I can't handle the noise of the Quaker but wish I could. My Sennie is very sweet, smart, outgoing & not phobic at all. I find most birds can be nippy. My Quaker was & so can Kiwi be, he's a baby & still testing with his beak but....
So I like both birds. And think both make good pets depending on the household & what you're looking for. Kiwi whistles tunes & is learning to talk. My Quaker didn't do either. But like I said, both make quality pets.