I've recently decided to pick up the remainder of the DLC I don't have (I have OWB and GRA). The question I have, is which way is more stable? Downloading the individual DLC or playing the Ultimate Edition?

It doesn't matter, the two games are exactly the same. They're just packaged differently.

Okay, I'm on PC, but...

I think there would be one other thing to consider. Running without all DLC installed, as that should give a small performance boost. I thought I read that there was a bug in the console platforms that prevents you from playing through all the DLC in a single play through, anyway.

Truthfully, the only reason I run all DLC is for mod compatibility. I can't stand the DLC's, I tried to force myself to play Dead Money the other day and literally fell asleep at my computer after a couple hours...nevermore..squawk...nevermore

Wherever you read that, if you did, it was wrong. I frequently run all the DLCs on one playthrough.

I believe the issue is with the PS3 console. I've read a number of posts where people recommend not playing with all the DLCs installed at once on that system. It create massive save game files, which impact performance.

I've seen it referenced a number of times over the years:

http://answers.yahoo.com/question/index?qid=20110602165832AAREbyq

https://www.google.com/search?num=20&safe=off&site=&source=hp&q=fallout+new+vegas+dlc+bug+fix&oq=new+vegas+dlc+bug&gs_l=hp.1.2.0i30j0i5i30l3j0i7i5i30j0i8i30l2.17612.37128.0.43118.17.17.0.0.0.0.359.5132.2j3-15.17.0....0...1c.1.32.hp..2.15.4477.n32aawEc5mE

Not something I've looked at closely, because I don't play the DLC, except rarely and briefly. I know I heard something about a mod to patch it on PC. But if it doesn't affect you, then it's not a problem.