If you look at the new Raid and Guild Leadership forums, you'll see that there's a fair amount of antipathy for Blizzard's new guild levelling scheme. There's a lot of small guild leaders bemoaning the fact that everyone wants perks, so they join the higher level guilds which have unlocked more perks.
While there's probably a little bit of perk-hunting going on, I think that most people are opting for higher-level guilds for a reason closer to the reasons behind Gearscore.
Gearscore was a weak proxy for raid experience which in turn is a weak proxy for effectiveness. People used Gearscore because they wanted to have successful pick-up raids, and didn't really have any other quick and easy method to evaluate strangers.
In the same way, people join guilds for new opportunities. Opportunities to meet new people, do new content, earn a high PvP rank, etc. People leave guilds when they feel they can't obtain those new opportunities.
Guild levels are a weak proxy for activity, which is a weak proxy for opportunities. It's not a big stretch to say that a Level 13 guild is more active than a Level 4 guild. There are probably more people playing regularly and actually doing stuff in the high level guild than the low level guild. And in turn, there's probably more opportunity to do stuff in an active guild than in an inactive guild.
Now, of course this may not be strictly true. For example, the raid team could be fully established, with no room for you. Or the players could be very clique-ish. Or maybe the tenor of guild chat is offensive to you.
But on the whole, that Level 13 guild probably offers more opportunities than the Level 4 guild. So people prefer to join the higher level guilds, even though they are not motivated solely by perks.
Of course, though, this leaves the same problem as Gearscore: how do you bootstrap yourself to a higher level? You need people to become an active guild, but people won't join you until you become an active guild.
I don't really have any solutions for that part.