I think it depends on the circumstances, but I had a horse who was lame without bute and we gave him devils claw - he was right as rain on it - worked miracles for him
My Tb with cronic arthritis in his neck is on 10-15ml of NoBute a day and is fine. I use it in conjuction with Cortaflex, a careful management routine and magnetic therapy. It didn't help an elderly pony with arthritic hocks on the same yard at all.
Seems to be luck of the draw. Also I think it depends on the type of pain - site specific pain is probably too severe for it to work.
I'd recommend trying it and after 2 weeks you should see an improvement. Oh and go for between 10-20ml a day not the 40ml max as I found it works better on a low dose.
We've used Devils claw with laminitics and its worked wonders. We can't use it on all though as one mare went loopy on it. My 40+yo mare gets it if she gets stiff/sore and we don't use "normal" bute at all and haven't for a good few years.
Its usually a try it and see it works for yours thing.
We used to give our ahtritic cob No Bute and yes, it did work. However, when our tack shop closed down we had to go elsewhere and found we could only get Bute Free by Gold Lable. It also contains MSM and Yucca. We were amazed at the huge improvement, so would highly recommend that (and it's cheaper than No Bute!!)