So far, SupportBee is winning on HTML email integration. Zendesk doesn't support it at all (and it's a long standing issue: https://support.zendesk.com/entries/80698-creating-tickets-f...). Desk.com does, but you have to view it in an overlay and inline images don't work. SupportBee supports displaying HTML email pretty much like GMail would. The only thing that doesn't work is inline images quoted in the reply message.
Zendesk and SupportBee both have very responsive UIs, but SupportBee's is simpler and maybe a little faster.
Desk.com is the only one that was able to ingest our existing support inbox, but it did a bad job of collecting threads into a single support request and did not include our replies in the tickets.
Zendesk is the worst for whole-company support due to its pricing model. Desk.com has flexible agents ($1/hour, billed in 5 minute increments) which is nice, but SupportBee's model of charging by ticket is probably the best of all for us.