To OP:
I was facing exactly the same choice as you were about 10 months ago -- the manual Accord Sport versus the manual Mazda 6. I am not a Mazda "fan", have not owned any previous Mazda or Honda vehicles. But I think you cannot go wrong with either vehicle.
My previous choices in vehicles tended to be high performance american V8s (I've owned a few: Mustang GT, Pontiac GTO, Charger SRT8, Challenger SRT8, etc). Those cars are (relatively) expensive and of late my primary concern has been lowering vehicle costs such as payments, etc. Previous to the 6, I was driving a slightly modified 2013 FRS (it had lightweight aftermarket wheels and the full Hotchkis suspension). I absolutely loved driving the car, superior handling, light, fantastic gearbox and torsen differential which (almost) made up for the lack power. Three reasons made me trade that car in: it was miserably small for a family car, it was incredibly loud on the highway, and I most important I wanted to get into a vehicle that could be paid off in two years or less. (If I could afford a second car for fun and/or autocross I would put that FRS on the top of my list). Also the replacement vehicle had to offer some amount of driver engagement and fun factor... even if only superficially. I give you all of the above to give you a background on my preferences on cars.
Prior to driving both I had essentially made up my mind that the Honda Accord was the vehicle for me. Among my top criteria-- it HAD to have a manual transmission. Initially I had briefly considered the Camry but ruled it out due to no manual and a significant number of reported transmission failures. CVT was NOT an option, so CVT being a dealbreaker, anything by Nissan was out.
I did countless hours of reading reviews and watching videos of both vehicles, but primarily focusing on the Honda. I test drove the Accord Sport several times both on highway and back roads. It seemed to have reasonably sporty handling (for a family grocery getter), good enough power for an I4, and had an excellent short throw shifter and the brake/gas were perfectly placed for ideal heel/toe shifting. That fact alone convinced me the engineers who designed the manual Accord had to be car guys.
I was pretty much sold on the Honda... then one lunch break I took a test drive in the Mazda 6. As compared to the Honda, I found the interior design and build quality -- especially the soft touch dash-- to be much more upscale feeling. Also I noticed the 6 engine seemed to be stronger...nothing earth shattering, but definitely distinct seat of the pants feel that it pulled harder from down low through the rpm range. The handling on the 6 is superior, more sporty and better composed when pushed hard in the corners. On the test drive I hit a tight 360 deg on ramp hard and pushed in all the way through the corner enough to scare the crap out of the sales guy in the back seat (who later confessed to me when I bought the car). And I think a 6 Touring would be a little better than the sport since it has 19" tires (IIRC, the Accord Sport comes with 18").
Also I liked the Mazda 6 engine a little better...there is not one thing I can put my finger on but it just seems more... responsive, slightly better growl, more eager. Mazda did a good job hiding the econobox roots of this car and give it just a little extra eagerness that makes it seem to want to play.
The car felt solidly built for an economy car, comfortable seats and good driving dynamics. And the deal clincher-- I got a fantastic deal on my, about $5K less than the Accord Sport (felt like I stole it).
As far as downside, there are a few but not many. I find the car noisy on the highway but for whatever reason it's all road noise, I do not have the wind noise problem others have mentioned. Hearing other 6 owners complain about wind noise makes me laugh actually as the FRS was the noisiest vehicle I had ever driven. By comparison the Mazda was almost quiet on the highway... don't get me wrong it's not quite by modern standard but it was a big improvement over the FRS. I did not drive the Honda enough on the highway for a good noise comparison, so if road noise is a big deal for you test drive both extensively on the highway.
The stock shifter is not as short and crisp as the Honda, and the pedal placement is less than idea for heel/toe... that being said you can still heel/toe it effectively. And the Corksport short shift kit and weighted knob made a huge improvement in the shifter feel. I believe the Honda gets to 60 faster than our cars because it will do that in 2nd whereas the 6 requires an upshift into 3rd... but if 0-60 is important to you, you are looking at the wrong cars. Overall I would say power is adequate but from time to time I would like a little more (so I will be doing the OVT tune, Corksport SRI and Racing Beats exhaust shortly).
I do have the "squeaky" front suspension issue (creak over low speed bumps)... this seems to be a common thing. Took it back to the dealer... they said maybe I was driving the car "too hard". When I pointed out that the issue only showed up at parking lot speeds or pulling in/out of a driveway the service manager just shrugged. The creaking is mild, and intermittent and only seems to show up in wet weather so far I just live with it...not a deal killer for me.
One thing I will say though: the Yokohama Advans that came stock on my 2015 6 are perhaps the worst tire I have ever driven. They handle just fine in the dry with predictable give at the limits, but in the rain they are downright dangerous. After 15K miles the tread on all 4 corners was over 60% worn and every time I drove this car in the rain I swear it was trying to kill me-- hydroplaning, skidding, torque steer, car all over the road. Worse than anything I have ever driven. Almost traded the car out but decided first to try new tires -- bought the Continental Extreme Contact high performance all season and haven't looked back-- superior dry and wet traction and handling. So if you get the Mazda 6 Sport do yourself a favor and plan on upgrading the tires.
Hey good luck -- and let us know either way what you decide and why.