Let me add a little value, from someone that owned a 2016 Mazda 3 five door, manual and has had Mk7 and Mk7.5 GTI's.
The Mazda is a different car, with a motor poorly suited to the manual. It hates, hates, hates to rev, 4500 is about where the fun stops. It's the worst naturally aspirated motor I've ever had, and the 2019 and 2020 still use the terrible lump. I routinely got 21 mpg, the thing hated gas. My BMW M Coupe got better mileage. Lots (or all) of this was the driver's fault. If that car had the motor from MS3, it would have been great. I've extensively driven the two MazdaSpeed 3's, and aside from being almost comedically heavy (300 pounds heavier than my 2016 for some reason, and 500 pounds heavier than the 2006 Mazda 3 I had before the 2016) they at least had a motor that liked to rev and felt suited to the manual transmission.
Okay, so the motors aren't comparable. The EA888 stock, or tuned is wildly more entertaining thing that actually likes to rev and feels more naturally aspirated than the Mazda 2.5L SkyActiv baloney.
But the Mazda had some serious pluses. It was way more fun to drive. Lift off oversteer was easily, predictably and repeatably available. The steering was more immediate and naturally weighted, however it was also EPS and had very little feedback, much like the GTI. The brakes had a different feel, maybe not better, but more linear under all but heavy use. It loved to be pushed hard, to and past the limit and provided very clear warnings.
The VW is a bit sterile in comparison. It's much more capable (the Mazda and my Mk7.5 are both on Michelin A/S 3+ tires), entry and exit speeds are higher, it's absolutely, in every way imaginable faster. The clutch feel is better (even if it's weak). Driven at 90%, the VW is much calmer, but it's that last 10% where the VW leaves me cold. It can certainly be pushed, forced to the limits and wash and repeat. But it's seldom fun in the way that the Mazda was. It's dry, clinical and composed. The Mazda was much more like my previous rear wheel drive cars, looking for chances to scare other drivers that you'd lost your mind.
I won't speak much about the style, I prefer the GTI, but did like the old 3 hatch, the GTI is a good bit smaller and holds just as much inside, if not more, and has rear air vents, a huge plus for my kid. The interiors were mostly comparable, the Mazda had more safety equipment standard and the blind spot monitoring worked much better than VW's. Plastics, pleather and carpeting were all similar quality. The Mazda had a painful amount of different finishes going on though, the steering wheel, door, dash and center console all had different materials that in no way tied together.
I haven't driven the newer Mazda 3, I hear the solid rear axle took the fun out of the chassis and the steering is slower now. So nearly all of what I just said is probably gone and the VW is just better all around. Pity, the old one was just a motor away from being great. However if it was as heavy and stiff as the previous MS3's, it wouldn't have been what I'd have chosen, those cars were not for me either.