You have 8 clubs, 8 diamonds, and 7 spades. So what works best? Why, no trump, of course. Lemme see how the field did. Five people in 6 spades and one in 7, heading the minus scores. Three in 6 clubs, all with an overtrick, six in 6 diamonds, five with an overtrick, one in 6 no, one opposing pair in 6 hearts, down 7 for the second worst score their way, and one bidding and making 7 diamonds!
There isn't a whole lot to be said about the bidding, except in reference to the spade suit, and perhaps a reference to the heart sac. Wait a minute. Hafta go back. They shouldn't be down 7 but six (minus 1400) in six hearts which is still worse than the minor suit slams, but beats the NT. Anyway, my first thought was that the (more nearly) balanced diamond suit would work better than the clubs, since you can ruff the third round of clubs. But on a heart opening lead, which you'll surely get, it isn't all that easy in diamonds, i.e., vis-à-vis clubs as trump. You won't have an entry to dummy (ruffing the 3rd round of clubs) unless you ruff before the last trump is out, nor would it pay to cash two rounds with the A K first, since then the J of diamonds can ruff higher than any trump in the closed hand -- except that, of course, when the queen drops you don't need a ruff.
So on this hand, I don't believe there is any significant advantage to the more nearly balanced suit as trump. The principal bogey here is the spade suit. I have cautioned my readers not to sneer, q.v., at the minors. Oh, of course if you bid 7-card majors over 8-card minors, you're bound to come out ahead on occasion. But I would suggest that you're going to be hurt more often than not, particularly at the slam level where you don't save a level in the bidding for a bonus as you do at game level. I've pointed out other occasions in recent weeks when 9- or 10-card minors were eschewed for a 7-card major where perhaps a 4-2 split or some other bogey dooms the contract.
Eight-card fits are traditionally the minimum for, um-m-mm, a freely chosen trump suit, as in the Stayman Convention, though of course 7-card fits are known to work not altogether rarely, and indeed, the "Moysian" (4-3) fit is often touted as playable, though I don't know if anyone has ever touted it for the slam level. At the game level, needing one less trick than you do in a minor, where you have no stopper in another suit, the Moysian fit just might work better than a slightly more robust minor. But at the slam level, where you don't save a level to get the slam bonus whether bidding a major or a minor and with so many points at stake, I would strongly recommend going with the safest contract, the suit with 8 cards over 7, or no trump if all suits are stopped. Here the spade-diamond holder took his partner out of 3 no to bid diamonds, and North, perhaps not anticipating the slam, preferred spades and now couldn't retract his preference. But he should have bid diamonds anyway. Not just more cards, but a top honor as well.
As for no trump, all I can say is that it beats spades for a reason I've often touted, which is that if your (presumed) strong suit doesn't pan out too well, you can often, not always, of course, switch to another for your tricks. But it's an awfully risky bid, a lucky make, and for my money, I'd be as happy in a minor suit slam.
The seven heart bidders? Why, of course I saw where they were going to lose a trick (beyond the necessary) as soon as I saw the lead, which was the 8 of spades. Yes, of course, the defense leads a third round of spades (actually punctuated with a few diamonds leads) and declarer ruffs low. Oh, please, Mr. Declarer. You've got five of the top 6 trump with only three trump out and you can't spare one for a ruff? You ruff with the king and lead low to the 10 9. How can you be hurt there?
But of course the bid was a loser from the beginning. Oh, it was close, or would have been with stellar play, and would have worked against a major suit or no trump. But they were in a minor suit slam and down six is too expensive -- though only by 10 points for those making an overtrick in their slams.