The Corolla is a transportation appliance, the Mazda3 is a driver's car! The Mazda is quicker (thanks to more power and the conventional 6-speed automatic vs. the CVT in the Corolla). It also handles better, has more supportive, comfortable front seats and has several features that the Corolla doesn't even offer. It's also worth noting that every review I skimmed of both cars mentioned that the Mazda has the "best in class interior in terms of design, materials and build quality".
The Mazda3 looks and feels like a significantly more expensive car, especially from the driver's seat. The Mazda3 is EPA rated at 30/41mpg (city/hwy) and the Corolla LE is 29/38. The real-world tests I have seen show that the more powerful Mazda has 1-2mpg better overall fuel economy compared to the Corolla.
The Mazda3 i Touring has a few features that are usually found on much more expensive cars. My favorite is the Blind Spot Monitoring with Rear Cross-Traffic Alert. It monitors your blind spots and it helps you back out of a blind parking spot by warning you of any approaching traffic. Rain-sensing-wipers are also fairly unique in this category, but they're also standard. Minor touches like the leather-covered steering wheel, shifter knob and parking brake handle with red contrasting stitching is one of the reasons that the interior looks so nice. Choosing the $1,100 Touring Popular Equipment Package adds the excellent 9-speaker Bose Surround Sound audio system, automatic dual-zone climate control, SiriusXM sat radio and an upgraded 7" touch screen for the infotainment system. It also adds a feature called E911 automatic emergency notification. If you are in an accident causing the airbags to deploy, the car will automatically use any Bluetooth-paired phone to call 911 and transmit your exact GPS coordinates.
One of my favorite things about the Mazda3 is the choice between the 4-door sedan or 5-door hatchback body style. The 5-door option has tons of cargo space (kind of like a mini-SUV), but the traditional 4-door sedan is available for those who don't want or need the space. It's also worth mentioning that the Mazda3 performed better in several crash test parameters and it the overall frontal collision rating is better also.
The Mazda3 will be a very reliable car and I think you'll be pleased with it!