Well, I certainly agree with Marrakai. I've owned both .400s. I prefer the 3" but either would be fine, although 3" brass seems to be a bit easier to find these days.

At any hunting range that a double rifle with express sights is suitable for, I would always opt for the .400 over a .375. The .375 Flanged Magnum may offer slightly more flexibility as the range increases, but must wear a scope to realize it. The lion's share of the reason I switched to doubles from bolt rifles was the sparkling handling and instinctive pointabiility of the better quality doubles, which no magazine rifle can touch. A scope just murders this.

I would not accept a double in the Belted Rimless Magnum under any circumstances.

Although I'm not knocking them, sidelocks have never been my cup of tea. I'd want it in a best boxlock, pre-war English only. 26" barrels only. If I decided to splurge a bit, maybe a droplock. The problem is that, while I love the droplock, I've never been especially fond of Westley Richards doubles.
--------------------------------------------------------------------------