Area 51

An interesting matchup... let's see. Both undoubtedly have a background in mathematics theory, although Berry would appear to be more able to put it into practice and together with his construction knowhow would probably have the edge. I'm not too sure how well Aldous would cope on a deserted island. There could well be a few cardboard boxes for him to cut with a wooden ruler, as is his wont, but would this help him in a mortal battle with an older foe? The fact that he would be apart from Mrs Aldous could inspire him, but even so I think Berry would win. And here's how:

Having constructed a large and deadly mousetrap from abandoned timber and steel, Berry lays a can of deodorant, salvaged from his luggage, as bait. Despite lots of planning and hypothesis, Aldous is mesmorised by the can, and is snapped in half as the chuckling, victorious Berry watches from a nearby tree.

By the way, I was going to apologise for my lack of activity for a week or so, but seeing as you were so late to reply I needn't...