For me it started with the outset of my story "Unwilling Eurydice". It was written at a point where Angel and Cordelia have essentially gotten over Doyle's death, and I kept that in the story. Which meant I brought a guy back who didn't really belong there anymore. Getting back in touch with friends you used to know well is always an awkward thing, much more than making new ones, so I wouldn't be surprised if Doyle preferred to hang with Wesley. And Wesley in his turn must be quite curious: this is the guy he heard so much about when he first arrived, yet never got to meet. Time to make up your own opinion.
Of course, this is just the start. Why they're sitting there talking to each other in the first place. You don't jump into bed with every guy you talk to, and you certainly don't declare your undying love for them. So, what else is there?
The way I see it, they're the right kind of combination of different and alike. They both like pubs, and they're both intelligent (Doyle cannot possibly have gotten his teaching credentials when "Hero" says he did, but if we're to make it fit even a little he must have skipped a grade or two). Both have a good knowledge of demonic hangouts and people. Actually, it seems to me that while Doyle didn't like his own demon, he rarely had a problem with other people's – ex-wife's boyfriend aside, and I think that had other reasons.
Wesley's a posh Englishman and Doyle's a working-class Irishman, and that part of the world still has a class struggle. Wesley's an ex-Watcher, Doyle is half demon, and if anyone thinks that is proof enough they couldn't get together, please remember which of the AI members knew of the demonic brothel.
We know Wesley had a crappy childhood, even though the details are mercifully spared us. I'm willing to argue that Doyle had a good one. This is in no way canon, so I'd like to elaborate: Doyle was a penniless boy with a good job. That indicates sheer willpower or lots of support. Now, when he found out he was half-demon, he let that ruin his life. I find it hard to believe that this would have happened if he made it so far because of willpower. (If this seems far-fetched, think of another poor boy that worked his way up through willpower: Lindsey McDonald. Would he have reacted the same way, or would it have made him even more determined? I believe the latter.) Although I can't prove anything, I find it likely that he did have lots of support from home, and that this added betrayal to shock. Mummy has helped me so much, and now I find she's actually been *lying to me* all along?
As indicated in "Billy", Wesley is afraid of the darker parts of his psyche, presumably something he connects to his father. Doyle is trying to supress his demon part, which was inherited from *his* father. So they have the "bad dad" thing in common. At the same time I for one have played with the thought that Doyle at some point in his life had a "good dad" as well (if his mother ever married).
Both boys are to a certain extent cowards, while they have very different ways of dealing with it. Wesley has a strong sense of duty, and tells himself that things have to be done, thus forcing himself to do it. Doyle makes sure everyone, including himself, are quite aware that he's not fighting anything, he's minding his own business, he's not under any obligation to do anything brave – and once that's settled he does it anyway.
They have both fallen for Cordelia and expressed crush-like admiration for Angel, but once again, they went about it in completely different ways. Cordelia was pretty open in her flirting with Wesley, and yet he needed to be called a blueberry scone by Giles before he dared approaching her. Doyle on the other hand was rejected repeatedly and refused to give up. As for their dealings with Angel, Wesley went with the "faithful servant" routine. Doyle teased him about his Batcave attitude. I don't think this indicates that Doyle is less serious concerning affairs of the heart, just more relaxed.
As long as it isn't about his demon side, Doyle isn't very afraid to open up. I'd say he spoke more about himself during the nine eps he was in than Wesley has done ever. But he's also ready to pay attention to other people's needs even if they don't ask him. Wesley's helpful, but cautious to offer help where it may not be wanted, which is shown for example in "Untouched", where he's afraid to offend Gunn by offering to pay him. And he's *extremely* quiet about himself. So in that respect, I would say their personalities work well together. Wesley can be of most use if he knows what the other person wants, which he'll usually know with Doyle, and Doyle isn't afraid to pry, which he'll have to do with Wesley.
And let's not forget the sidekick loving. :-)