Higher frequency penetrates less. Higher the frequency, more line-of-sight connection is needed.

Operator run wimax basestations can use much more power. For example 3G basestations can have 40 W or even 60 W antenna power. High power transmitter needs network planning and guarantee that nobody else is using the same frequency. That's why operators need lisenced spectrum.

I guess that wimax has better channel coding than 802.11b/g which would mean slightly better performance. But 802.11n (the new wi-fi) is giving the same promises for consumer level wireless network. Given that I haven't seen any wimax basestations for consumer market and 802.11n-draft basestations have been sold "for ages" means that most likely 802.11 is the way for homes.