I've been to Austin and lived in Dallas. Both are nice places, but I do know a lot more about Dallas than I do about Austin.
Their weather is very similar despite their being about 200 miles apart. In general, it's very hot during the summer with little to no humidity, and it does snow during the winter, or, at least, it gets cold enough for it to do so. Summer and spring thunderstorms are fairly frequent and tend to appear with little warning, save that of meteorologists ("If you don't like the weather in Texas, wait ten minutes."😉, but they're often short lived. Dallas is located in Tornado Alley, and Austin's been known to get its fair share of them as well; it's not as bad as you might think, though.
Geographically, they're both very flat, and I swear the sky seems closer. Both are highly populated cities with toll roads and traffic, but it's really not that awful.
As far as things to do are concerned, there are two Six Flags in Texas: one in San Antonio and one in Arlington, a suburb of Dallas, and Schlitterbahn, "America's #1 Waterpark," is in New Braunfels, close enough for a day trip from Austin.
When someone says Dallas, they generally mean Dallas/Fort Worth, or the Dallas metro area, which is rather large. This area has lots of toll roads (notable is George Bush Turnpike), and though you can easily get around without them, it is often much slower to go this way.