There are several considerations. First off, anything you deep fry will take on a different flavor. I can attest specifically to hops in beer batter tasting wildly different and, in my and my dinner guest's opinions, disgusting. I would likewise be concerned with a heavier malt like a porter or stout.
Flavoring is really not the responsibility of the beer in the beer batter. The desired flavor (in my opinion) is that "deep fried breading" flavor that makes fried food so delicious. Other flavors just distract from that. In addition, you may also be concerned with imparting flavor to your oil. If you reuse oil repeatedly, then you want to fry things with as little flavor as possible, seasoning them afterwards, if at all. (Though note for beer battered fish! Once you deep fry fish you can't re-use the oil for anything that is not fish! However, I use beer battered vegetables as a side-dish frequently for big summer cookouts).
So, all in all, if you deep fry for larger groups several times a summer, you want a light American lager. Little flavor, plenty of carbonation, enough alcohol, and cheap to boot. I use Budweiser.