Short summary (from memory, so might be a little faulty):
GPLv3 = GPLv2 + you can't sue any users/distributors for violating your patents + you grant an implicit license to all your relevant patents to your users + you must protect users from patents that might be covering code you contribute
For companies with patents and lots of patents they are afraid of losing their ability to sue for patent violations. I'm unclear whether the license you grant is just for the GPLed code or just in general. And in general it's unknown how all this plays out in court, so most lawyers (and thus companies) avoid v3 like the plague.
AGPL = GPL + must distribute even if you just provide an internet accessible service.
The idea being that the GPL only applies to distribution, so if I modify some GPL software but never distribute it (because I just run it on a server I control) I never have to GPL my changes. The AGPL says you have to distribute/open source your changes even if you don't distribute if the modified software is accessible over the network to users.