The advantage of an auction is that it gives every team a shot at acquiring every player. If you really want Durant or LeBron, you can have them, so long as you're willing to spend the money for them. You don't have to rely on pure luck to get the first or second overall pick.
To me, it's demoralizing to go into a new fantasy league and get like the 7th pick and you know you've probably already lost your league.
A lot of people are hesitant about the auction format, especially if they've never done it before. The best thing for them is to go do a mock auction or two to get the hang of the format. That's all it takes. After that, you'll probably find it addictive.
It looks like ESPN custom leagues have five scoring formats:
1.) Roto - teams in say, a 10 team league, are ranked 1-10 in each of the 8 statistical categories. This finds an absolute winner and doesn't have a playoff IIRC. The plus side of this is that you don't get screwed for having the second best statistical week in the league--and you went up the guy who had the best.
But the negative is that you lose a playoff and you lose a lot of the intrigue that head to head creates. Still, this is the most common format apparently.
2.) Head 2 Head: Each Category - you get points for each of the 8 categories you win against a weekly opponent you match up with. So say he wins 5 and you win 3 of the categories, then your record at the end of the week is 3-5. If we don't do Roto, then I would strongly recommend this format.
3.) Head 2 Head: Most Categories - you get a weekly matchup, the guy who wins the most categories gets all the marbles, electoral college style. i.e., if you win 5 out of 8, your record for the week is 1-0. You can also tie in this.
The big disadvantage here is it potentially rewards highly unbalanced teams and encourages "category punting." For example, you can field a team entirely composed of completely awful free throw and 3 point shooters and still win and get full credit because you loaded up on scorers and rebounders and shotblockers, etc. You can't do this well in roto each category formats. Going with each category scoring is also nice because it keeps more people into contention deeper into the season and you get credit for having teams that are really good at certain things.
Finally, 4.) & 5.) are Points-based and H2H: Points based formats. I've never done it this way before, and I'll say up front I don't have a ton of interest in this format. What you do is assign points to certain stats, fantasy football style. i.e., assists = 2 points, rebounds = 1 point, & turnovers = -1 pt, so on and so forth. I don't really like this format because I feel like it's hard to come up with a good set of scoring that isn't arbitrary/biased towards certain stats, and I have a hard time seeing how shooting percentages play into it. We should stick to the categories or roto formats instead IMO.
My personal vote is for either a Roto league or a Head 2 Head: Each Category league. Either one are good to me.