Which is better?

Disc clutch is almost always better because it offers more contact area for mating surfaces and a more positive lockup. They are also typically easier to adjust without removal, which may or may not be important to your performance... That said, a well-tuned shoe clutch matched to your application shouldn't be any slower -- just more finicky to work with and tune. That's my $0.02.... ~Ted
X2 A Draggin-Skin drum clutch will perform every bit as well as a disc. Adjusting it is a bit more difficult than a disc, generally lighter, parts are cheaper too. Heck, the whole dang clutch is about half the cost of a good disc clutch. JMHO
A disc engages much quicker. BUT if you are low on money get a drum...save your money for tires. I've seen guys win on drums vs discs
From our own experience the only difference I can see is on the starts. The disc clutch seems to be a hair quicker than the shoe. Once up and going however I see no difference. I prefer the disc simply because of adjustability and life. The shoe clutches are cheaper and when they are worn out simply buy a new one where as the disc clutches you can do a rebuild. We ran our shoe clutches all year (blue clone class) even when we could have switched to a disc and had good success with it.
I like the disc clutches best. I just got back into karting this year, but use to run Bully clutches. I got an AKRA and was told that the drums were fine for the motors. I ran the drum for about a month and a half and sold it. I was getting killed on the starts and sometimes it would chug. I maintained the clutch like the instructions said, but never could get it to quit. Might have just been a bad apple, I dont know, but I threw my Bully on from 2007 and have been running it the rest of the season and still going. Just my .02 cents.
on starts a disc will bite better and will be easier to fine tune. once they are locked up a clutch is a clutch. so if you are on a big track that starts are not that big of deal a drum will work but if it's something that is a tight track, hard to pass and starts are critical I'd spend the money to get a decent disc. not $400 but there are a lot of used discs out there to be had for 1/2 that.
You can pick up a good disk clutch on here for close to what a drum is gonna cost you to get right. I would just try to get one that would accept drivers that are available to you. But make sure whatever class your going to run alllows a disc. We race 2 different tracks in the same class one is a open clutch and one is drum only so check around as to where your gonna be going.