I myself am a Gamma (SEE-Fi).
Alpha- It's not that I don't like them, it's just that I don't really agree with how they carry themselves. When I'm with an Alpha one on one, it's usually fine. I think that the NT-SF bond is still there, but in a weird way. I find myself criticizing a lot of what they do internally, and fundamentally not understanding why they do a lot of what they do (Alpha NT); or think that the things that they do are a bit pointless, or missing the point (Alpha SF). Some Alpha NTs I know are extremely respectable, good people. One of my good friends is actually an LII. I really can't say anything bad about the guy at all, but I think we have to suppress some of what we normally do, or kind of joke around about it. We play games together, and I'm the guy that gets really, really mad and really aggressive at times and it can kind of irk him, but I tend to joke around about it to soften that. And sometimes I will make some mistakes because I didn't think things through and he'll comment on that, but then again he jokes around about that despite super Ti'ing me.
Beta- Betas are usually the quadra that I have the most issues with. It seems like some betas are dramatic just for the sake of being dramatic, and I don't consider myself too dramatic a person; and my non participation in their "beta-ness" kinda makes me the odd man out sometimes. Beta NFs can come off as being excessively flirty, needy, or teasing. They seem to create this air that they are "Desirable" so that their Beta ST buddies can come in and give them validation. Beta STs can come off as being overtly logical, bossy, and hard-assed for no reason. Betas seem to care a lot about social norms (what the individual sees those as in their heads), and I have issues with this because I don't really have much of a sense of social norms, my socializing is based on the individuals I'm with. Betas can be pretty cool people, but they can be a bit of a handful sometimes with their style. I'd call them pretty "excess" at everything.
Delta- I tend to very much enjoy deltas. They can be very chill and relaxing to be around, and great conversationalists. I enjoy the sharing of values, and the fact that talking about value related stuff isn't really awkward with deltas. Deltas are the kinds of people that I think would be great to live with, they are non pushy and keep to themselves for the most part, but then enjoy socializing sometimes too. The only bad thing I can think of about deltas is that they lack that "edge" that I seek in people. They just aren't the same as Gammas, but I still like them. A lot of my friends are Deltas.
Gammas- Well they are my quadra, so what can I say? Gammas can be just as picky with their own quadra as they are with others. I've known some gammas for a VERY long time before actually opening up to them; and other times we just kind of start talking to each other and figure out that we're similar and things are cool. Since I'm pretty similar to other gammas, everything goes really well as long as the person I'm talking to isn't a jerk. Gamma NTs are a joy, and Gamma SFs are pretty cool, but differing values can really get in the way of my accepting them sometimes.