I own both pistols... first came the Buckmark Bullseye, I've had it for over 10 yrs. The friendly shop where I bought it at let me go through what they had on hand to choose the one I felt had the best trigger pull.
It has shot everything from Remington "econo brick" ammo to CCI Stinger and Winchester Super-X HV hyper velocity ammo without a hiccup and accuracy has been superb. I haven't used any match or subsonic ammo.
I have two M41's, a standard 7" bbl and a 5 1/2" heavy barrel and have only had them for about 4 years.
The 7" bbl version was first the first one, the trigger is slightly crisper than the Buckmark, and so is the grouping at 25 yrds, but it is not all that improved over the Buckmark, in my opinion, considering the price difference between the two.
The 7" bbl doesn't like the brick ammo, and it more sensitive to different types of ammo, it shows a definite preference for Federal ammo.
The 5 1/2" has been temperamental in the kind of ammo it is willing to digest and has been a real disappointment, to where I hardly use it.
I bought the M-41 after reading about it here on the forum, and on it's reputation. It's all steel construction versus the Buckmark with steel and aluminum alloy, and is more refined in it's manufacture.
Since I don't do formal match shooting, the Browning Buckmark has met all of my needs. If not for the influence of the forum, quite honestly, I could have easily lived without the M-41's... but it is neat to own one as there is a certain sense of prestige and "oh-wow" factor associated with owning a M-41 that the Buckmark doesn't enjoy.
There are times when I wonder if the ammo sensitivity that seems to dog the M-41's is worth the hassle.
The Buckmark does have an array of after market performance accessories available to trick it out, if you want to.
So, that's my experince with the two brands of pistols. Both are capable of accuracy better than what I'm capable of producing. Making a comparison between the two, to me, is analogous to comparing a Dodge Viper V10 and a Ferrari V12. Both are more that capable of getting you from point A to point B quick, fast and in a hurry... with one costing a lot more money and being more refined.