I've owned both, and I much prefer the Stevens. Accuracy, and quick follow up shot capability on multiple coyotes were the deciding factor for me.
My Handi was not what I would call a terrible shooter, but it wasn't real good either. I reloaded, trying many different combinations of bullets, powder, brass, primers. I tried various accurizing tactics, all with minimal improvement. I've done nothing to my Stevens, outside of camo painting. Finding a good load combo took very little time. I can nearly cover my groups with a dime on a regular basis.
IMHO go with the Stevens.
Dave