Well, you're in luck because I have owned both. I had a 2005 Mazda Mazda3 S with the 2.3 liter and 5 speed manual that I drove for about 50,000 miles before I sold it and got a 2011 Suzuki Kizashi Sport GTS with a 6 speed manual. All Kizashis come with a 2.4 liter engine.
Now keep in mind that generation and model year will make a difference regarding which Mazda3 you are comparing a Kizashi to. I strongly recommend you get a SkyActiv model given the technology really elevated Mazda in every way and further departed them from Ford.
While I'm sure there are notable differences between a newer Mazda3 and the first-generation model I had, I can say this much about a Mazda3 vs. Kizashi:
The Kizashi is a heavier, more refined vehicle that I certainly consider a small mid-size rather than a large compact, as some would say. The car drives much more like the midsize sedans I've driven compared to the compacts that I have. The Kizashi has much better noise isolation and is much more comfortable on longer trip. Everything from the suspension to the seats aid in this. It's also got noticeably better build quality and if you compare the same model years, I think you will see this between the Mazda3 and Kizashi. The Kizashi's real rival is the Mazda6, not the 3, though by size and dynamics, it's more like the Mazda3. The Kizashi is a unique in-betweener.
That being said, the Mazda did have some advantages. First of all, the manual shifter in the Mazda was hands-down superior to the Kizashi's. Mazda is famous for their excellent manuals and it was very noticeable. The transmission also seemed to be better paired to the engine in the Mazda thus it was livelier than the Kizashi's 2.4 mated to the 6 speed. However, keep in mind the Kizashi easily weighed about 500 lbs heavier than my Mazda3 so that's a factor.
Handling-wise, again the Mazda3 had a bit of an edge. It was a bit more nimble given the lighter weight and it also had hydraulic power steering instead of the Kizashi's electric. That being said, the Kizashi handles very well and considering it's significantly more refined and comfortable than the Mazda3 I had, the handling difference wasn't too considerable.
In the end, the better car is based on what your priorities are. If you want an economy car that is as close to a sports sedan as possible in fun factor on a budget, then the Mazda3 is better. It's simply more fun to drive with the better shifter, better engine-trans pairing, and more nimble and agile dynamics. There are also more aftermarket parts.
If you want a more refined car that's significantly more comfortable on commutes, long drives, yet offers a lot of nimble handling and fun-to-drive character, then the Kizashi is the winner. It sacrifices a little as a heavier car but offers much more in terms of being a "grand tourer" than an econo-sports sedan like a Mazda3. The best test of this was driving all day. I was exhausted after several hours in the Mazda3 and my passengers never complimented the comfort. The Kizashi on the contrary is a car I can drive all day and still feel fine and I always get compliments on its comfort and handling in grand-touring sort of trips. I literally get people falling in love with my Kizashi from the back seat.
I moved on from the Mazda3 largely because I wanted a more comfortable vehicle for my commute with noticeably better build quality and road isolation while not sacrificing too much in drive dynamics for a good value. The Kizashi nailed it for me and I never regretted moving on from the Mazda3 to the Kizashi. It's also been more reliable which isn't too surprising though the SkyActiv Mazdas are said to be the most reliable Mazdas to date. Mazdas will have better support and parts as they are still around unlike Suzuki. Pros and cons, but comparing just the cars, the Kizashi is the winner. I realized this back in 2012 and still think the Kizashi is the better car for the money.
2011 Suzuki Kizashi Sport GTS 6MT (Black)