What does a "quality" running top do that a Tesco top wouldn't?
Cheaper fabrics aren't as breathable and don't wick sweat away as effectively, so you get hot and sticky quickly. Then you also get cold if you carry on going, as your clothes are wet and clammy rather than dry. That's the main difference IME.
That and the fact they generally fall apart in the wash faster, so don't stand up to as much use.
Other differences are that cheaper fabrics are heavier, tend to be scratchier, and have labels and seams that chafe. This isn't a massive deal if you're just doing a 30 min jog, but can make a huge difference on a 3hr long run (like bleeding skin sort of differences!)
Finally, better quality stuff tends to have more features (key pockets, thumb loops etc) that are designed properly and actually work. I've had enough of key pockets that don't hold keys, tops that flap at the bottom and make your stomach cold, or those awful side pockets on leggings that - if you put anything in them - interfere with your running gait.
When I first started out running I got away with supermarket kit, but now I train most days, and over much more mileage, I need decent stuff. And happily, that doesn't necessarily need to mean spending more money. Lots of Decathlon stuff is good, and v reasonably priced. But if you can afford Ronhill or Inov8 in the sale, then all the better. I have Ronhill tops that I was training in a decade ago that are still going strong - so in the long term, quality kit is a better investment and more eco friendly too.