I've been using moly for around 20 years +/-, and HBN maybe 12-15 years. I can't think of another product that has created such a decisive divide between those who love it and those who hate. my experiences using moly have been very good. There are a few applications where I feel moly excels and a few where I feel it adds little or nothing - and maybe even provide an undesired outcome.
I found that I get the best benefit from moly (and HBN) in my high-volume varmint rifles (both bolt guns and A/R's). On a good varmint day, I'll shoot perhaps 400-500 rounds out of one rifle, running a bronze brush through perhaps 8 strokes and perhaps five wet patches and two dry patches at 250 round intervals. In the A/R's, I'll also quickly disassemble the bolt carrier, do a quick clean and lube, reassemble and go. After several days of this, when doing the "deep clean" after the hunt, the barrels clean up very easily as compared to having not used moly. Copper will still build up, as will carbon, but to much less of a degree - especially the copper.
As far as the moly making the barrels last longer, I will disagree with anyone saying a barrel will last 25%-50% longer, though I do believe the barrel remains just a bit cooler due to reduced friction. Throat erosion and barrel wear is possibly slightly delayed by the use of molly as a result. I have seen NO ill effects to my barrels from having used moly. The throats still get cooked and fire cracks do form - just as with any other barrel. If anything, they are delayed, not accelerated from the use of moly.
When folks say it is hard to clean moly from a barrel, it is most true in older barrels with fire cracking, the moly being difficult to extract - just as carbon is difficult to get out. Carbon is far harder to remove than moly. To remove moly from any newer bore without any deep fire cracking, a nylon brush wrapped with a patch and JB Paste applied and run in and out of the bore a few dozen times will remove all trace. Shooters Choice or Butch's Bore Shine have worked well for me, as well as the Pro Shot products.
The second reason I use moly is on target rifle ammo which I jam. I used to occasionally dump powder into my action when unloading live ammo which was jammed. Seeing how that is a big match ender, I found that using moly, I have been able to avoid the powder dumps, as the bullet doesn't stick into the bore. Keep in mind I "soft jam". If one were to hard jamb, especially into a really worn, fire-cracked bore, it might still get stuck. I don't do either, so I'm not sure. I do know for a fact the odds would be less than not using moly.
Downside (Target shooting). Regardless of all the folks I have listened to, my best results were obtained by doing a good cleaning as often as one would do if not using moly. When using moly in my bolt target rifle, I ONLY do the molly to keep my bullets from sticking. By starting with a clean gun, shooting six to eight foulers and I know I'm starting with the same "barrel condition". The downside here is NEEDING to fire those foulers. Some guns won't shoot right till a dozen rounds are fired. For me, I'll pay that price in a rifle where the jambed load is worth it. If I have a load that does not require jamb in my target rifles, I often don't use moly. I'm not concerned with being able to shoot hundreds of rounds in a day without good cleaning as I do in my varmint rifles.
Downside (A/R's and other semi-autos). Moly, being very slick stuff, creates too much neck lubricity in .223/.556 bullets of small weights (like 40 grain and under) AND in .20 caliber or smaller - regardless of bullet weights (other than possibly 50 grain in .20 cal). The reason is there is too little surface bearing area of these small bullets in small diameter necks to adequately provide tension when moly is on the bullet. The bullets will tend to slide into the neck a bit when the round is pushed over the feed lips and the ramp while loading off the magazine. I found this occurrence no matter how much tension I applied to the neck. This could be solved with some bullets by crimping, though that will usually kill accuracy and few small bullets of 40 grains and under are suitable to crimp. In short, using moly on 50 grain or higher bullet weights works very well with few surprises.
I've read "horror" stories of folks not being able to go back and forth using -and not using -moly loads. Stories of how their rifle never shot the same and such. I think once folks have shot moly in enough situations and learned of what works and what doesn't, they might be a bit more open minded on it.
