The gravity and atmosphere of Mars make it a more ideal candidate.

True but isn't the big problem self sustaining food, water and breathable air?

Sure, but this conversation was Mars vs. the moon. The only argument the moon has going for it is that it's a short trip.

Mars does have a reasonable atmosphere (albeit not breathable, it's mostly CO2), and therefore does have some hope to be terraformed to earth-like levels. We will probably have to use closed systems (greenhouses with water recycling) until we heat the planet up a bit and get it back to the state it was when it had running water and precipitation.

A near-earth asteroid might be a better choice.

I'm not degreed so this is just my off the wall thinking but asteroid mining yes, definitely. I still think we need a Moon base, need to show we can run it successfully for around 2 decades then start seriously planning a Mars mission. As a kid, I'd have imagined we'd already have a successful Moon base.

Asteroids, since I assume they move and possibly in odd orbits might be difficult to reach in emergency situations, I'd rather not see any nation's Astronauts stranded on a remote asteroid.

Most asteroids' orbits have the same characteristics as those of planets.

The problem I would see is finding a big enough NEO asteroid, that you actually can stand on instead of floating by its side, or having to worry about reaching escape velocity if you jump strongly enough.

If one's willing to go to any asteroid, not just NEO, then Ceres could be a possibility. A quick search says the delta-v required to reach it from LEO is about half that to reach Mars' surface.

I was thinking that having a few feet of gravel between you and radiation would be useful for a base, as well as the ease of coming and going from a smaller body.

I suppose it would be helpful to build some kind of centrifuge in any base to simulate gravity, as well.

Mars has lots of water and the ability to make rocket fuel and oxygen from the soil.

The moon has a weaker gravity well to escape.