Try to have a festive German meal for Christmas Eve if you can -- roast duck with red cabbage and potato dumplings would be traditional. Is Spaten open? They do a great one. Kaisergarten is a nice place too-- good to know they open on Xmas eve!
Definitely -- I like Brenners but Kaisergarten is a much more intimate and festive place. They also have very nice food, and unless Brenners is doing something special for Xmas I think Kaisergarten will have a more traditional menu.
Oh, also check out Zum Alten Markt, it's right near you. They seem to be doing a special Christmas menu, and if they are open for Xmas eve that would definitely be my first choice. Cute little place, tiny, family run, and very good kitchen.