Overall, I'd say Studio, just because thats how most artists few their music, as a full on studio project. Rather than a live experience alone.
BUT
To be 100%, Its on a track by track basis for some artists. Theres versions of songs I prefer live over studio when its more Guitar solo based like Buckethead. Whom is my favorite solo guitarist. His songs are varied SO much compared to his studio stuff. Every time he performs a live song, its performed differently and often times better than his studio stuff.
Examples:
Nottingham Lace (Studio)
[youtube]iyKpoh1YHew[/youtube]
A great song nontheless. But it sounds very much studio here. Very planned out, clear and precise.
[youtube]vYxrdrzmuUw[/youtube]
But live, its raw, very freestyle at certain points. And theres MANY sections not in the original that I love so much. Observe points:
3:36 that very small variation is what I mean of the perfection of BH live
3:57 BH gets his Van halen at that moment with one hand
5:20 BH goes into the main riff of the song but distorts it slightly and it is amazing
5:40 & 6:04 he uses my favorite of his Techniques with the killswitch button
Now in the contrast, Theres a Buckethead song I enjoy better Studio than Live
Final Wars (Studio)
[youtube]DTsi3g5s-zs[/youtube]
Overall this is a better song in studio, but the specifics or why are:
:14, That shredding riff is just amazing, And adds to the song. Its missing in the Live version.
Final Wars (Live)
[youtube]G7INzkhGTyE[/youtube]
at :20 the riff isnt there. Its small, but big music fans break down music second by second, and Im one of those types of cats.
1:36 is MUCH harder and darker in the studio version
2:25 is missing the awesome Killswitch technique that the studio one has
I dont hate this version AT ALL, I adore it, I just prefer the studio over it at certain parts of the song. And vice versa
This shows what I mean by the track by track difference of Live and studio, It depends on what's being talked about, ya know.