I spent a couple thousand hours operating the Aztec and 310 before I moved to the 414. Flew Navajos (turbocharged) in there as well. Spent some time flying a RAM IV T310R (a real hot rod) and have had some others in there.
Basically, a turbocharged plane works its engine(s) harder. You've got more heat, which will tend to lead to lower service life, more issues. You've got more parts to fail in the turbo and the associated controllers. The exhaust is under more pressure (literally, since exhaust pressure feeds the turbo) and are something you need to be more concerned about. Not sure about support or parts on the Twin Comanche as I believe those turbos were all aftermarket, so that might be a consideration. Most of the time turbocharged engines have a more complicated fuel system since the fuel nozzles are pressure balanced and you have more expensive fuel pumps.
After spending a couple thousand hours flying the Aztec and 310 around the country without turbos, I was pretty used to flying in the lower altitudes, in the soup, etc. that you get. In a non-pressurized turbo aircraft you're wearing cannulas or a mask at the altitudes where the turbos really do you any good, neither of which are particularly comfortable and the novelty wears off. Lycoming engines I find generally hold up better to turbochargers than Continentals, but that's not to say they're trouble-free. You will sometimes get some really great tailwinds up high that are worthy of Facebook/Instagram posts, but the reality is that most of the time you'll notice the headwinds more. Yes, you can get above a lot of the weather a lot of the time and get some smoother air, but even my wife up at FL450 in her Challenger has to deviate around storms.
Personally, I'm not interested in owning a turbocharged plane again and generally advise people against buying them. More maintenance headaches, and generally fewer benefits than you'd imagine. The exception to that is if I flew over the Rockies regularly where the extra altitude is beneficial to avoid cumulogranite. However, I've crossed the country coast to coast (including over some tall rocky sections) with the 310 and the Aztec, naturally aspirated, just fine. You just have to do a bit more careful planning which, frankly, you probably should be doing anyway in a piston aircraft.
The one exception would be if I got offered that RAM IV T310R at the right price. That, I would buy. But that plane is just awesome.