I host with both - Dreamhost for a few years, Hostgator for about a year
Actually, I currently host with BlueHost, DreamHost, ANHosting, HostGator, PixelGate(don't ask), Lypha, and GoDaddy. HostGator has all the others beat. I'm slowly migrating my sites over to them.
Dreamhost was recommended to me by the teacher of a design class I was taking a few years back. I agree with a previous post that said Dreamhost is good for smaller sites, but HostGator is better for business. Here's why:
I (and my clients) had serious problems broadcasting perfectly legit email lists because Dreamhost was contantly being blocked by AOL, MSN, and other major email providers for violations of spam policies eminating from their servers. This can be very detrimental to anyone trying to run a business - not so much if you're just emailing your family and friends.
I also had some serious downtime issues with them for about a year. At one point, I mentioned to one of their support techs that I was transitioning to HostGator and they simply said "Honestly, I don't blame you".
I've had good experiences with the support offered by Dreamhost, but in all honesty, HostGator has them beat hands down.
As for speed, I had several clients comment on a noticable increase speed when I moved their sites from DH to HG.
My vote goes to HostGator. Best host I've ever used.