The PC Engine's CPU is probably its strongest aspect, Hudson did a great job here. Going with a really fast 8-bit CPU makes much more sense than Nintendo's choice of going with a slow 16-bit CPU, especially when the screen is 256 pixels wide so most of the calculations a game would be doing are only 8 bits anyway. Even when you have to do 16-bit calculations, the SNES CPU still has an 8-bit data bus so it doesn't have much of an advantage over the PC Engine (all 16-bit operations take extra cycles compared to their 8-bit counterparts). In practice, fast action games like shooters play a lot more smoothly on the PC Engine than on the SNES. This problem is exacerbated by the fact that the SNES CPU provides the option of running at ~3/4 speed if the publisher didn't want to pay for faster ROMs, so a lot of games have unnecessary slowdown because the publisher wanted to save 50 cents per cartridge.

Where the PC Engine ends up weaker is in the video processor. That generation of consoles was able to do more with the video hardware than previous generations (like the NES and Master System) due to faster RAM becoming available. The PC Engine used the additional bandwidth to make it possible for the CPU to access video memory while the screen is being drawn, while the SNES kept the restriction that you can only access video memory during vblank and instead used the additional bandwidth for more background layers. Being able to access video memory all the time is definitely a useful feature, but the result is that PC Engine games often look more flat than SNES games.

As someone who owns a SNES and a TG-16, I think I disagree. The TG-16 graphics really pop compared to the SNES.

The SNES can only render 256 simultaneous colours. The TG-16 could do twice that at 512. Its video processor was also full 16-bit.

I’m not sure where you’re getting that the video was the weakness of the TG-16. At the time, that was the Turbografx’s whole claim to fame in that it was superior graphically to the SNES.

Source: Old enough to remember the commercials and bought both consoles to compare like nerds did back then

Remember that the PC Engine came out in 1987, over three years before the SFC did. That makes Nintendo's CPU decisions even more questionable, but also explains the huge gap in graphics hardware - not just more background layers, but also effects like transparency, scaling and rotation, and richer colours.