We are doing this, with a pullout on the right side and a regular door on the left. One good reason not to do a pullout on both sides is that you need space on one side at the back for plumbing and a disposal if you have one---if you do a pullout on that side, it has to be a shallow one (just the front half of the cabinet, basically), so you lose space at the back. If you just have a door, you can use the little shelf organizers and such and tuck extra things back there.

We have not decided 100% on the pulls, but are leaning towards bar pulls placed horizontally in the middle all of the cabinets so that they look consistent. I've seen people do knobs, though, and I've also occasionally seen people do it so that the two sides don't match--main rationale for that is, I think, that it's immediately obvious that you're supposed to pull out the trash vs. swing open the door. I like the consistent look better, though. HTH!

We have the same: a pull-out on one side, and a regular swing door on the other.
I decided to go for the uneven look: bar pull is horizontal on the pull-out, vertical on the swing. I wanted to make it clear to visitors how each door worked, as artemis78 suggests above. It works for us, and someone actually complemented us on doing it that way. It's also consistent with the rest of the kitchen: lots of horizontal bar pulls on drawers, but verticals on doors.