Honestly, your experience in any city will be dependent on your own wants/needs/attitude.
Texas Medical Center and in particular, UTMB is one of the world's leading Cancer and Heart institutes. Take it for what it's worth, but if you have no connection to the medical world, so be it. That's not to say hospitals wherever you are aren't good, these are just very good and co-located for one hell of a system.
I'm actually quite surprised that someone said that DFW is more diverse than Houston. I would contest that, but also would consider that several areas of either city are probably more diverse than others. On the whole, I have always thought Houston was more diverse.
The food in Houston really is quite outstanding. I bet DFW has more high-end places, but the vast array of cuisines and options are quite staggering, accessible, and really fantastic in Houston. Don't forget that Houston's craft beer industry is just booming with both homebrewers and business entrepreneurs alike.
I agree that DFW definitely has better public transportation. Houston's public transportation is built to take people in and out of the city during rush hours and that's about it. It's actually very good at that, but as a public utility or use for anything else, it's not very good.
I also agree that a large portion of Houston's economy is based on petroleum and energy, but don't forget that Houston is the 4th largest city in the nation. The diversity of industries in Houston would surprise you. The spectrum is pretty vast with oil/gas/manufacturing to high-tech nanotechnology (Rice University is one of the big leaders in nanotechnology).
Houston is one of a few U.S. cities (and only one in Texas as far as I know) with permanent, professional resident companies in opera (Houston Grand Opera), ballet (Houston Ballet), music (Houston Symphony) and theater (Alley Theatre). (stolen off the Westin Hotels website, sorry, I couldn't remember all of the pieces).
The Houston Zoo, Theater Under the Stars, all the museums as well as the Menil Collection, the largest privately own modern art collection in the nation are all here as well.
I absolutely think Houston gets a lot of crap because it's just not good at promoting itself in the least bit. The PR of Houston stinks, but if you take a bit of energy to go find what you like, you'll probably find it here, unless it's mountains or something like that.
You'll definitely need to deal with traffic, but what large city doesn't? It's really hard to say one has worse traffic than the other considering that it depends on where you live and where you work that makes your commute. A lot of these things (in any city) are manageable through different means.
Political climate is even interesting here, obviously we're still Texas, but is there another city in this state that has an openly gay mayor? That could be good or bad for you, but it's interesting that it happened.
For me, I truly believe I'd probably make a happy life for myself wherever I go. We tend to find the same kinds of people and activities that we enjoy no matter where we are. What matters to me in general is that I find a job where I enjoy the people I work with and am doing something important to me (if I'm lucky of course). Along with a loving spouse and friends/family support, I think any place will be great for you - even Dallas or Houston