Almost any urban place you live, your exact location will affect your outdoor lifestyle a lot. I've lived in Cambridge MA, without a car, and it was like being in prison. But I lived in Waltham on the west side of Boston, and X-C skiing (canoeing/kayaking for those with the gear) were a short drive away... but the area has gotten more congested since.
I lived 16 years in Albuquerque, and was mainly stunted by my nose-to-the-grindstone attitude. It was nice to be able to X-C ski in the morning till April or May (on Sandia Crest), then have a warm afternoon. Nights in the summer were rarely above 70F, days in summer rarely above 95F. But except for backcountry skiing, the outdoor ops seemed farther apart than in Vegas.
Now I live near Vegas -- but on the far west side, maybe 15 minute drive from Red Rock (I've run out to the visitor center and back), 45 minute drive from access THs to the near-12000' Charleston. The city is annoying -- I go to the Strip about once every 2 years, then usually to pick up a guest. But I've never lived anywhere where it was so easy to pick a large variety of outdoor activities, mainly because of the central location.
I have to chuckle at Dow's comment about the lack of an outdoor community. It all depends what you want. I don't do rock climbing unless it's required, but know lots of informal groups that go every weekend. There are some very active and large outdoor meetups in the city, and there are folks at REI and elsewhere who do hairy back-country skiing in the local mountains. Like any place, you have to get connected.
Heat in the summer? I used to run in summer at the heat of the day; but I live where it is ~4F cooler than downtown, and knew the location of every leaking sprinkler and hydrant and water fountain. In summer we head to the Spring Mountains, other high NV ranges, or even the Sierra-- which are as close to us as they are to LA, time-wise.
I definitely would pick Vegas over Phoenix. I like the Superstitions, but they are deathly hot much of the year, and there aren't many places close by to escape the heat-- which is even worse then Vegas, when the relatively humid air rolls through AZ in the summer. Phoenix is more civilized in some ways, but is about 4x the area, and has absolutely severe sprawl.