That's a tough call.
We (the devs) have spent much more time working on the Patapon2 version than any other, so I'd say we know this game better than the other ones, and for this reason HBL works generally better on the patapon exploit. Plus I dont own HSG2, and I think JJS doesn't either (not sure), making development fo this exploit a bit more difficult than expected.
6.31 has new nids and I'm not sure we found all of them, JJS updated some of the "lib" files, but I'm sure there's more work to do, so for now, the 6.31 firmwares have probably less homebrew compatibility than 6.20.
It's a matter of personal choice, I think. As far as I know, no game requires 6.31 for now, so if I were you I would stick to 6.20+Media Go for your official purchases.
However if you want to play online badly, I would say upgrading might not be a bad choice.
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