Bearing 'looseness' would not cause binding. Quite the opposite. Binding would imply that the preload is too tight, or the bearings are worn to the point where they are not turning freely. In the worn case, you would probably hear a 'growling' noise at speed, which might come and go when you turn one way or the other.
It is also possible that the shop set the right side correctly, and the left side spins more freely because it was not adjusted. Check that one for excess play.
As others have said, it is normal for the brakes to drag somewhat until there has been enough rotation to push them away fully. Severe brake drag (usually coupled with premature wear and often warped rotors) implies a problem. It is difficult to prove that a bearing is binding without removing the caliper. A bearing with too much preload will make the hub area of the wheel much hotter to the touch (than the other wheel) after a moderate to long drive, and it will eventually suffer premature failure. Of course, a dragging brake will have the same effect, so perhaps that is not useful in this case.
Either bearing brand is excellent. These things will last virtually forever if resealed and repacked every 100K miles or so. Both sets should be replaced at the same time. For the labor involved, it would be silly to do just one set. I have had very bad luck with the fit of the aftermarket grease caps. They are just a bit too large, and the process of forcing them on resulted in metal filings being shaved off the cap. Had to replace much of the grease to be safe. Very annoying. Save the original caps if possible.
Best of luck.
1986 300E 5-Speed 240k mi.