I'd save the Sears ammo. While some ammo collectors spurn it, it's a sign of a past long-gone. I feel that such ammo will grow in value soon, when folks look around and realize they don't see it anymore.
Just 10 years ago you'd see an occasional box of Sears or Montgomery Ward ammo at gun shows. I haven't seen it in nearly that long, though. I suspect that it got shot up and the boxes tossed.
Common ammo can become collectible when it is no longer readily obtainable.
Don't think so? Have you priced a box of World War II-era .30 Carbine ammo lately? Or a full box of military .38 Specials dating to the 40s or 50s?
I have a full box of Remington 12 gauge plastic shotgun shells an old guy gave me. Few would recognize it, but this was the first 12-gauge cartridge to employ a one-piece, plastic wad. That little tidbit, and the fact that the box and cartridges are like-new, add value.
Sears, Montgomery Ward, Smith & Wesson, Alcan and other makes of ammo are getting scarcer every day because people shoot them up.
Trade your ammo to a collector, or salt them away and wait for values to rise. A new box of .30-30 cartridges won't set you back much.