I've been running the Briley rail on my #1 1301 for a couple of years now.
#1 is a Gen1 1301 with the normal magazine tube. I have a Nordic +2 extension on the gun.
The Briley does a magnificent job of keeping your hands away from the barrel when it's hot. This is especially useful if you are doing short-stocking demonstrations, which I almost always do with an 870 anyway. So there's that.
It is held on only by the magazine tube extension. If I was buying a 1301 today, I'd prefer to buy the normal length mag tube and add the Nordic extension just because of how reliably it stays in place. Once the Nordic tube is tightened down, it stays tight until you decide to take it off. All it requires is normal finger pressure to do both. It stays tight even after a full day's worth of shooting full powered shells. It is a truly splendid piece of equipment. All my magazine tube extensions are either Nordic, Wilson, or Vang Comp because I have found all of them do a splendid job of staying tight while shooting, which is immensely helpful in keeping guns from breaking.
I haven't seen anyone using the Briley on the new extended mag tube models to see how the plastic cap fares. But I can believe it wouldn't be as trouble-free an experience as the Nordic extension.
When I bought the Briley it was $200 bucks. I saw it show up on their site on December of 2020 and I thought I had some instructor revenue I could burn (better that it be used on necessary equipment than taxes) so I bought it.
It is fantastic for mounting an X300 at exactly the spot I want it. When combined with a section of rail from Arisaka Defense, it keeps the light nice and tight into the overall profile of the gun.
It was a stupid expensive way to mount an X300 at $200. It is a lot more stupid at $335. It adds a considerable feeling of bulkiness to the fore-end of the gun which most people who pick it up don't like. Personally I don't feel like it added much weight to the gun, but that is a totally subjective assessment as I never weighed it. My #2 1301 is lighter, certainly, but it also doesn't have a mag tube extension on it either. So personally I don't find the weight a problem, but I'm not carrying the thing very often. I mostly pick it up, shoot it, and put it down. I may be holding it for 30-45 minutes at a time demonstrating manipulations...but I do that with an 870 and the 870 is considerably heavier so I don't really notice.
So is it a worthwhile modification to your shotgun?
If you want something that shields your hand from the barrel
and lets you mount a light and other accessories exactly where you want them
and you don't mind the fore-end feeling at least 1/3-1/2 more bulky than the factory fore-end
and you are perfectly happy to drop about $400 to get all that going for you, the Briley will do all that.
If you do not answer an enthusiastic and happy "Yes!" to every single one of those questions in that order, probably best skipping it and buying a glove for the left hand instead.