First of all, the 187 BIB is better served with a 1-in-12 twist. You can probably push them so hard as to blow them up with a .300 Win Mag & a 10-twist; you certainly can with a .300 Ackley. A 1-in-12 will also stabilize the old 210 Berger in the large cases & I'd imagine it would stabilize the newer 210 as well.
But as German says, the before any recommendation could be made, we have to know the type of shooting. I'm going to make a rash assumption: since this is a benchrest forum, you're talking abut benchrest.
One note: The 187 BIB has won far more than its share of the matches in which it has been used. This in spite a ballistic coefficient of about .520 (measured, doplar radar). And many of these matches occurred at Hawks Ridge, where the wind is always a big factor. The moral is to correlate this sort of data (historical performance) against another kind of data (theoretical advantages) such as developed by German Salazar & posted on the 6mmbr.com site.
As for the chambering itself, the only reason I'd pick the .300 Win Mag over the .308 Norma Mag is that in Europe, you can get RWS brass. In the States, I'm sure the .300 Ackley & similar variants is the most used 30-caliber chambering. However, based on the number of people who use it and their number of wins, an 88-grain water (full to overflow) case outperforms it. That includes the .308 Norma Mag, and the .30 caliber wildcats based on the 8x68 case.
If I lived in Europe and were shooting 1,000 yard BENCHREST under IBS or NBRSA rules, for a .30 I would use a wildcat based on one of the RWS cases -- either the 8x68 case, or the 9.3x64 Brenneke case. The downside is having to put up with a wildcat, the upside is no belt. Barring that, I'd use a .308 Norma Mag, and if concerned about case life, I'd turn off the belts for an other kind of wildcat.
In spite of the popularity of the 6mms and 6.5s, I believe if you look at the number of BENCHREST wins -- and look at both score & group, particularly at ranges notorious for their wind, the .308 caliber magnums have a decided lead.
FWIW