As far as I'm aware, Yubikey 4 and Yubikey Nano 4 can do 4096; the older ones like the NEO can only do 2048.

Not that 2048 is flawed as such: it's still north of 100 bits workfactor at the moment, as far as I gather. 3072 would be equivalent to about 128 (similar to the EC algorithms secp256r1 or Curve25519), and 4096 is some extra insurance on top. (As a benchmark: Snowden used 4096-bit RSA keys for GnuPG.) Anything bigger than that could introduce OpenPGP compatibility troubles.

All of these are secure when correctly implemented. (Yubikey use NXP chips. I don't have much to say beyond that, I haven't audited them.) All of them will fall to Shor's algorithm on a quantum computer of sufficient size, but we're not likely to have one of those for a good few years, if they're possible.

I picked up two of the github keys. Never did get them working under OS X. Plug them in and nothing, not recognized by any of their tools, no new keyboard recognized prompt, nothing. Anyone else have trouble with them on OS X?

No, because the github / U2F keys don’t have any writeable local storage.