My favourite team in terms of fun to play is chaos. Skavens come close.
However, for a tournament or a short-term league, because chaos have expensive rerolls and no starting skills, I prefer wood elves who start with everything that's necessary.
Chaos are fun not so much because of their bashing power, but rather because of their development potential - everything, whether +ag, +mvt etc. is good and additionally EVERY player has access to strength skills (skill access is a crucial aspect of team development, making all elves and dwarves also favoured in terms of long-term development). And chaos have no flaws so to speak (e.g. everyone has ag3), which goes hand in hand with the fact that every stat increase is good.
Along the same lines, CWs make excellent runners with their st4 and their not so major lack of speed - that's why CWs are my favourite players overall.
And mutations are fun!
=> Did I make my case for chaos clear enough?
Skavens have gutter runners who are excellent players yet still reasonably cheap. Mutations also allow for lots of crazy agility related stuff. Unfortunately, I find that team hampered by only ag3 linemen. More generally, I personally never count on a team with no ag4 players to get any decent "running around", and even more so ball-handling, at least for a tournament / short-term league. I've had so many matches where I kept on rolling 2 when picking up the !*Y@#T(**!&#*&!_@!!%R%?@*(!!! ball when playing humans or chaos. Skavens have those gutter runners, but their throwers only have ag3, and their linement cannot dodge around.
Hence my regular decision to go for elves if I really want to win games. And wood elves are the most able at stealing the ball from the opponent, turning him over and over again, because of:
1- their speed (skavens also have it, but don't have matching agility, so they cannot go to as many places as WEs).
2- their wardancers - give them strip ball, and every cage-reliant opponent will cower in fear until all possible his ball-carriers get sure hands. By which time your two wardancers will also have gained tackle

.
But theoretically, every team, except from the really weird ones (let alone little guys teams, i.e. gobbos and halflings) that is those fresh from the experimental stage, i.e. khemri, vampire and ogres, can win matches. Some will struggle more at tournaments because of the lack of skills, while others will do better for low TR but will have limited development (e.g. the Norse). Try as many as you can and see which ones you feel the best.
By the way - wood elves, chaos dwarves (because of their combination of hitting power, speed and cheap players + cheap rerolls) and orcs (you know why...

) are IMO the most common winners at tournaments. Skavens are also reasonably good contenders.