I've spent considerable time in both cities.
Weather -- definitely Albuquerque. Four gentle seasons, with a wee bit of snow in the winter, and a dry but hot (but not Las Cruces/El Paso/Tucson hot) summer with intermittent rain. Austin is hot and humid, perhaps more so than Orlando.
Culture and urbanity -- Austin, Austin, Austin. Albuquerque's downtown is essentially dead, and except for the Old Town and Nob Hill areas, there's not too much nightlife. Austin has a thriving downtown, an exciting local music scene and a more bohemian culture; it seems like more of a college town than the Duke City.
Austin is, ideologically, more leftward leaning than Albuquerque. New Mexico is thoguht of as a Democratic state, but that's attributed to the large Mexican-American population, lower incomes, and large percentage of PhDs. There's a large military influence in Albuquerque, but it's not a place where people thump their Bibles particularly hard, like Colorado Springs or Charlotte.
Both Albuquerque and Austin have more "funkiness" than a similarly sized city, but Austin more so.
The built environment of Austin a few of the less desirable traits often found in Texas cities (i.e. frontage road development, high rise signs, etc.). Albuquerque has the South Side barrios, where zoning is merely suggestive, and Central Avenue (the city's main street) is astill a bit sleazy.
New Mexico is called the "Land of Entrapment," both for of the enthusiasm of the local and state police when it comes to enforcing speed limits, and the fact that the state jsut sucks you in -- it's tough to leave, and if you do you're inevitably drawn back in again.