As someone who got his start playing multiplayer shooters with fucking Doom (IPX bitchzzzzz), the server browser model annoys the fuck out of me. It is occasionally pleasant if it a given server is private and tied to a large, healthy community, but even then it feels stagnant when I am playing the same ten players all the livelong day, and usually on the same three or four agreed-upon maps. It's part of why I haven't been able to get solidly hooked on TF2 at any stage, even through a private server someone I know owns.
In the conventional server browsing model, games feel slapdash, with people dropping in and out, the teams constantly unbalanced, the same dudes donging on everyone over and over, everything at the whims of the server's owner, blah blah. It's like Halo customs, but forever. Jumping into a server fifteen minutes into a game and playing out the dying seconds of an all-but-decided game on a team of six (half of which is a bunch of regulars shredding everyone) versus a team of four is fucking dull.
Matchmaking, for all its flaws, makes the individual games feel more important, and exposes you to more players, more gametypes, more maps, more variety. Sure, people drop out and the teams are often imperfect (but given the complexities involved, the system gets it right an impressive amount of the time: I've played more "50-49" [or equivalent] games of Halo 3 than anything else I can name), but on the whole it feels more like a sport: you're there from the kick-off, and the experience is likely going to be competitive.
Dedicated servers? Yes, please. Server browser/searching for customs? Fuck. That.