I use both
Sears rinses better, but maybe it's just my kid or something, but Tide seems to remove grease better. (She loves to wipe her greasy hands on the front of her clothes) Dirt, mud, sandbox stuff, Sears appears to handle don't know if better.
Overall happy with both, like the fresh not overpowering scent of Sears. Have been using Tide Coldwater Free lately as well, though a liquid, which I seldom use; I like the results very much.
Main reason I ever tried Sears was recommendations from this site. Tide powder is very sudsy, Sears is not. Tide regular has a powerful scent, Sears does not.
Liquids, The Tide Coldwater regular has a very strong scent but lesser suds, The Tide Coldwater free is just right, no smell, little suds, have no complaints about "left behinds" even in the cooler water.
I still wash my whites in Hot/Cold with Sears