For me, the biggest and most defining difference was speed. On Dreamhost, my downloads were capped at like 200KB/s and uploading via FTP was capped at like 50KB/s. With Vidahost, I download and upload as fast as my connection will allow. I thought it was just my slow connection back in Canada but even after I moved here and had a much faster connection, the transfer speeds were the same.
Also, the site I had is now long gone but it was noticeably quicker on Vidahost.
Stability was another. Pretty sure they both have 99.9% uptime but I noticed my Dreamhost account down far more than Vidahost (couple times a month with dreamhost, so far, never with vidahost). I use it quite frequently throughout the day.
The reasons behind my experiences could be as simple as being on a crap server with Dreamhost but I would certainly not go back.... though I do miss the quirky newsletters they would send out.