I've loaded and shot the Hornet a lot in the past 25yrs.
I've used most of the available brass.
The Remington is OK but runs a little thicker and lower capacity (except for some old UMC stuff I picked up in the '70's that had been factory loaded "who knows when!").
It also tends to have a little more runout on the neck thickness. But not too bad for most uses. I have some (100) nickle plated cases but have only one loading on them with some cast bullet loads, so I can't really comment on them yet, but they're pretty loaded with a 35gr V-max stuffed in them!!!!
Winchester is usually the best and what I would recommend. It seems to be consistent from lot to lot, and generally show a little less run out than the Remington.
Oddly enough, the best brass I've run across is some Sellier & Bellot that I've got from some factory ammo I bought at a bargain. The only problem I had with them is that the firing pin hole is much smaller than the U.S. manf. brass and required turning down the decapping pin to keep it from sticking in the case. The holes were very consistent and weights varied very little. Loads with these case will run 0.2-0.3" smaller than ones fired from the others.
Get the Winchesters, and try the Rem. 45gr HP bullets on top of 10.8gr. of Hodgdon's LilGun. This load runs 2750fps from my Ruger 77/22 KBZ (24"BBL) and shoot 0.75"@100yds. For max accuracy, try the 40gr Sierra HP with 12.5gr of LilGun-gets 3000fps!. Also try the 45gr Hornady "Hornet" with 11.5 of AA-1680. My most accurate load though, is a 50gr Hornady SX with 10.8gr of AA-1680 and a WinSP primer in the S&B brass. Only gets 2475 fps but often puts 5shots in one hole !! I've also found that seating the bullets close the the SAAMI figure of 1.720" except for the pointed bullets, where I use 1.750 (1.775 for Nosler BT's) for best accuracy. If I seat out to touch lands, the run-out affects accuracy negatively.
Good luck !
"There is no such thing as a second place winner in a gunfight" Bill Jordan