Darren: this is supposed to be about HIM, not you, right? So we should consider which of the two HE will get more of a kick out of, correct? Of course you are tagging along, so your needs do count...
But you've played both many times already, right?
I gather money is no object? Neither of these places is cheap for the foreign visitor, so unless you have some way to soften the blow, both will be very expensive... but Turnberry is extremely so. This should be kept in mind. Of course one only lives once and should not put a price tag on life experiences, but still, full disclosure is a good thing too.
So does your brother even care about "architecture"? Not many golfers do... If he's demanded that it be Open courses only, well... it seems to me he's not gonna care if he misses some cool Colt bunkering or a redan here or there or anything else of the architectural sort....
How old is your brother? I think one has to be at least 35 or so to have the requisite historical appreciation for Turnberry, given the greatest thing ever to happen there occurred in 1977 (Nicklaus v. Watson). Seems to me most want to play the course to relive THAT, or to take in the fantastic views, and play the oceanside holes....
Sorry for all the questions. But it helps to get this all straight before one gives recommendations.
And based on all of this, if my assumptions are correct (I'm thinking he's younger and doesn't care about Jack v. Tom that much), I'd say take him to Troon. Far more cool things have happened there lately, not the least of which being the most recent Open. It is fun to try to recreate what one has seen on TV, and that will work much better on Troon than on Turnberry. Troon also offers a wonderful 36 hole day, with golf on the Portland and the Old course with lunch in the middle, which makes for great fun. Troon does have much more of a "club" feel also, as opposed to Turnberry which is most definitely an American-style resort. That is, the course surely is a true links, and not American at all, but all the surroundings really do remind one much more of Pebble Beach than Muirfield, if that makes any sense. I'm thinking your brother will get more of a kick out of the Scottish club than the fancy resort.
BUT... this is all trumped if your brother is 35+ and especially if he is a fan of either Jack or Tom. If that's the case, take him to Turnberry. One simply has to see that in person at least once if one is a fan of either of those golf greats.
So you can see I made not a single comment about the "architecture" of either course. Why? Because to me it's a wash - they are both fantastic golf courses and really equal. That being the case, one makes one's decision based on extraneous factors.
TH