Here are a couple of pics from my old MPS that I owned back in the day:
I can impart some judgement here since I used to own a Mazda MPS 3 and am now onto my second Megane 3 RS (I had a Megane RS 250, sold that went to a 2015 Wrx STi, then saw the error in my ways and bought a Megane RS 265).
The Mazda was 'faster' in a straight line... if you like that thing. The MPS obviously has a bigger motor and higher engine HP. Thats the only thing going for that car.
Renault know how to build good drivers cars. Chassis tuning is obvious and you'll notice it instantly as soon as you drive the Megane. The MPS was hard to get on the power when there was even slight steering angle in the steering. So you were always waiting to get the steering wheel straight before applying power. On a track or twisting roads, the car is a lot slower than the Megane.
Megane also has factory LSD, Brembo brakes, and (depending on which car you buy) leather Recaro's. They are big ticket items that most other manufacturers leave out. The Megane is also newer too by about 4-5 years to your old car. The difference in interior feel is obvious, the Mazda is showing its age now.
Ask yourself this, what motorsport does Mazda compete in? None. Renault on the other hand is in all forms of motorsport and all that research/development filters down to their road going cars - especially the RenaultSport vehicles in the Renault brand.
I'll say this, I wasn't a "car handling" guy before I bought my first Megane. I never wanted to do track days or anything like that. But as soon as you experience a well set up chassis'd car like the Megane you'll understand. The car flatters you and makes you a better driver than what you are.