I love the Amiga. It's the system of my life. In a way, it helped to shape the person I am today.
Having said that, I'll also say this: Back in the day, I never owned a PC-Engine of any sort but I got to test the TurboGrafx-16 that was on display at the local Makro store. This should have been in the early 90's. It was definitely before the A1200 came out and I think the SEGA Megadrive was also a novelty. I remember finding the games incredibly well made (for an 8bit. I knew it was an 8bit despite the 16 in its name. Currently I refer to it as "the 8bit wonder"), the lack of loading time was also a major plus (having had a Spectrum, an Amiga and an overpriced, overpowerer and underperforming PC, i was soooo used to loading times), it had - at least apparently - better FPS/horizontal scrolling, the media in which the games came were great (the HuCards are no longer or thicker than a credit card. no need to worry about swapping slow, complex, underspaced, cumbersome and fragile disks), etc. I also remember that the price wasn't all that expensive and the gamepad was cool. I tested some Shoot-em-up and some Sports games that, honestly, I can't recall the names now.
Based on that first experience - which was positive - I have since tested several PC-Engine games via emulation. From that I was able to say that the PC-Engine (in whatever form you choose to address it as) IS better than the Amiga in some things.
So, without trying to go into technical mumbo-jumbo that frankly I couldn't care less about, I'll say that for pure arcade gaming the PC-Engine seems to be the best machine. The Amiga is better for everything else (strategy games, simulators, "serious" gaming in general) and, of course, it's much more versatile. So, if I had to pick just one, it would be the Amiga, but even with all the emotions related to it still raging, I am still able to see that the PC-Engine had more colours on screen, had faster scrolling and was overall better at making arcade games (as is epitomised by the Street Fighter 2 game).