I had a BPS 10 gauge and an Ithaca Mag-10 that I used for goose hunting. That is, until 3.5 inch 12 gauges starting to become more popular. I definatly noticed a difference in pattern, range and "knock down" between a 10 gauge and 3 inch 12 gauge, but the difference between a 3.5 inch 12 gauge and a 10 gauge was much less defined.
Ithaca made a version of the Mag-10 called the "Roadblocker". This was essentially the same shotgun with a 20 or 22 inch barrel, sans a magazine extension. It was designed to take advantage of the power of the 10 gauge slug against vehicles. Which HP White discovered in the 70's was quite an advantage indeed...
Eventually, I stopped using 3.5 inch guns. The only time I use them anymore is for pass-shooting geese and for turkey. . Otherwise, good shells/choke/shooting can make the most out of 3 inch 12 gauge shells. The type of pass-shooting I generally do is such that 30 yards is a "close shot". When you are laying in a cornfield-grave, shooting over decoys you probably could get away with 2 3/4 BB or BBB. The extra shot is also advantageous for turkey hunting. While its nice, plenty of people hunt this stuff with 12 and even 20 gauges.
Where I used to live, 10 gauge shotguns were still popular and stores like Walmart and Kmart stocked ammo for this gauge. Since the 3.5 inch 12 gauge got more established, this ammo selecton would shrink and shrink. I cant remember the last time I saw 10 gauge ammo at a retail store, even at places like Cabelas...Since you can still find 16/28 gauge, 10 gauge is out there but there are fewer loads that are harder to find and more expensive.
Whatever possible advantage 10 gauge might offer over 3.5 inch 12 gauge, only a very small number of hunters in a small number of situations would ever notice the difference. Use quality tungsten/bismuth shells with adequate shot sizes, proper choke selection and good shooting/hunting technique and you will have no trouble "making it rain" with 3 inch 12 gauge. Suffice to say, I don't really "believe" in 10 gauge anymore and my "love affair" with 3.5 inch loads is pretty much over with...My SBEII and Supernovas/Novas have 3.5 inch chambers, but its a P.I.T.A. to keep this non-standard ammo around. Its way to easy to stuff a 3.5 inch shell into my M2/M3 Tactical.
Also, have you ever fired a 3.5 inch 12 gauge BBB/T/F/000 buck/Slug or equivalent 10 gauge loads? Its a boderline religous experience and is probably the harshest recoil that many people will ever feel...
Since 10 gauge ammo is expensive/hard to find/barely necessary, you don't hunt waterfowl*which is 98% of the reason to own a 10 gauge* and that its a BPS and you are looking for a "conversation piece" I would pass. The BPS is a great pump, I love all of mine but unless they are a "highly finished" firearm, they arent much of a conversation piece. I don't remember if I have ever seen a BPS-10 that wasn't black/synthetic.
If you want a conversation shotgun, get a "punt gun" or hang an IAC 1897 "trench gun" with a bayonet above your mantle.