how badly distorted are newer digital cameras?

As badly distorted as any other camera ever was, given the same parameters. Unless the sensors are really poor, the distortion comes from the lens. So if you shoot with a wide angle lens, you are going to get distortions. Same with a telephoto, but it is not as obvious.

Generally, the more you spend on a camera, the more you are getting a higher quality lens that will minimize distortions. But there are some things that the quality of the lens can not overcome, and the best, most expensive super wide angle lens is still going to produce some distortions.

Any "distortion" would come from the lens being used, not the camera.

And lens distortion ranges from darn near zero (for typical "normal prime" lenses) to outrageous (for "fisheye" lenses).

If you're talking about lens distortion, there is a wide range. You get what you pay for. As far as pixelation, you also get what you pay for.