IIRC, the Ballard High Wall is machined from an investment casting. It's a nice action, and they make a nice rifle, but IMO the Meacham is a step above it in quality, just as the Ballard High Wall is a step above the European imports.
I own a couple of original Winchester 1885s, and a couple of Meachams. The Meacham is a 'blueprinted' 1885 built the way Winchester would have if they had CNC equipment back then. Everything is dimensionally perfect, the actions are extremely smooth (like an original Winchester 1885 or a Krag) due to the 8160 steel and the fact that they are really case-hardened, not just case-colored, and there is no slack or slop... just that incredible bank-vault-door feel as you work the action.
Steve Meacham has made a couple of improvements... smaller firing-pin hole, a stock through-bolt... just as the master gunsmiths of the Golden Era did when building a fine rifle from an original Winchester. All of his parts are interchangeable with original coil-spring 1885 actions.
My Meacham 1885 Low Wall .22LR schuetzen is the most accurate .22 rifle I own (and I own more than a dozen, including Kimbers, Winchester 52s, and a Turbo Specialties benchrest-based silhouette rifle). On a calm, clear day I can regularly shoot sub-1" groups at 100 yards with Federal UM1 ammo (and my Lyman Targetspot 20x)... although the schuetzen stock is a bear on the bench.
If you want a rifle that is better than anything Winchester (or Pope, or Schoyen) ever put out, then get a Meacham.
***
By the way, I am selling one of my Meachams, a silhouette model with extra-fancy wood, double-set triggers, and two barrels... one a .40-60 Maynard (.40 caliber on the easily-obtainable .30-40 Krag case), the other a .45-70 barrel. The gun has been test fired only. I have too many rifles, too many safes, I don't think I'll ever shoot BPCR, and I have another Meacham on the way (a Low Wall for small game and varminting). This rifle has a replacement cost of around $4,000 and an 18-month waiting list, but I'll sell it for $2,800 plus shipping to your FFL.