I'll agree with Chuck (except about good aikido = good judo, I don't know enough about either to agree/disagree).
I'm studying Tomiki Aikido now, but I did do Aikikai a few years ago (gap in between due to injured knees) and I'm more impressed by similarity between the two than any differences..
Essentially, from an initial practical angle, I found 3 major differences to a beginner practicing:
1 - Tomiki style favours evasion as the first part of the technique, whereas there's a higher propensity towards defending your centre without evasion in Aikikai
2 - There's a better structured way of learning ukemi in Tomiki Aikido
3 - Most techniques are done from grips in Aikikai, and from a strike in Tomiki
These are based primarily upon my experiences at 2 dojo, so may be peculiar to my own circumstances. BUT, the two styles tend to converge to a common point at the highest levels - after all to quote Jun (and myself from e-budo) Aikido is Aikido, styles don't really matter all that much, since the principles are the same across the board. I'd suggest just concentrate on seeing what this new spin on Aikido you'll encounter can teach you..
As to Tomiki being all about being competitive, very few of the people at my dojo have any desire to enter shiai. We see kakarigeiko as a way of testing your Aikido, but it's always, always, done in the spirit of cooperation. We help each other improve our Aikido..