I have a few of each, it may be a matter of preference OR what you believe in.   For me, low walls run circles around the 44's and I like the feel- one LW is a coil spring the others are a flat spring.   I did spend a little more time and money on the LW's so that may give them the edge.  Here's another case, I loan the 44's to folks I attempt to hook on this sport and one individual that shot a lot of comp prior to this, ran circles around me with it - go figure. 
Greg

Each can be made to work well, so buy the one you like the most, or better yet get both!

Currently finishing a low wall .22 to go with a couple of Stevens 44 1/2s in 22 RF.

I think the Stevens may have more drop at the comb so personal fit might be a consideration.

FWIW (probably no much )

For me as for leadball. it comes down to the barrels.  If both barrels were pristine inside (a BIG assumption at the prices quoted), I'd fall back on Stevens' well-earned reputation for having very accurate barrels far more often than not.

That being said, to second GT, for that kind of money, why not by both?

Bill Lawrence

I shoot a Steven's 44 and with the right .22LR ammo it is highly accurate out to 200 meters for .22BPCR silhouette.  With it I've shot several master scores.

FWIW, I've spoke with several Win. Low Wall & it's somewhat of a crap shot with some very accurate and others no so.  Based on those comments I'm of the general opinion that the barrels on some of the older Win. Low Wall were not up to snuff but I do not have direct experience.  Although the barrel was in like new condition, a shooting friend had a very nice older rifle relined.  He could not get it to shoot well with any ammo he tried.  Lee Shaver relined for him and it was a tack driver afterwards. The more recent ones are reported to be good shooters.  As to what constitutes an old or newer one I have no idea.

BTW, the Steven's design does have a potential problem.  If the shooter is not careful how the rifle is held when ejecting a case it can fall into the action & get stuck behind the breechblock.  After it happened a few times with me I've learned to cant the rifle to the left when ejecting.  I don't believe the Win. Low Wall has the same problem but I'm not sure.

Wayne