If you drive like a grandma on the street, probably not.

If you corner aggressively, or just want the extra grip available for when you might need it. YES.

Of course, the Potenza you're talking about isn't exactly the highest performance street tire out there, either. Still, I'd expect it to be way better than anything with the General name on it.

Keep in mind that consumer tire ratings have everything to do with the expectations of the reviewer. The person buying a General tire probably has low expectations, and if they don't go skidding off the road, they're happy. The Potenza buyer is likely to have higher expectations and if the tire doesn't perform well, it's going to get lower ratings. For this reason, I'd consider similar ratings between the two tires to be BETTER ratings for the Potenza. If the Potenza raters were rating the General, they'd likely have rated it lower. (I'm sure I could have said that with fewer words)

Look for things like the Tire Rack's actual tire test reviews with facts and figures. If they're not testing the tire you're looking at... there's probably a reason. If it's worth having, they've tested it.