There are a couple of things that can make a TV mess up on an Apple II or II Plus. First, composite NTSC video is 525i, 30 frames of 525 lines each second interlaced in 2 fields of 262.5 lines. An Apple II generates 262p at 60 frames per second, which is pretty close to NTSC, but each half-frame is the same, and there's a half-line missing. Analog sync circuits mostly lock to this without a problem. Later digital sync circuits get messed up by the missing half-line.

Color TV sets have filters designed to roll off video response before 3.58 MHz, which is the color subcarrier frequency. This is pretty low video bandwidth, corresponding to about 200 lines horizontal resolution. Some sets use comb filters which allow video bandwidth up to 4.2 MHz, but which again don't like the un-interlaced Apple signal. They count on the color burst phase changing 180 degrees every line, and the Apple II doesn't.

So a Sony or other top line TV from 1977 will look pretty good. A 1990s TV with digital counters for sync won't lock very happily. A composite monitor like one of Apple's or Commodore's is next best to RGB, and RGB adapters for the Apple II are rare. LCD TVs are digital and most won't lock to an Apple II. Even Apple's own blue & white Studio LCD, which has a composite input, will not display Apple II text, although it will display graphics.

The IIgs with a gen-lock card is a different matter. I understand it is capable of true NTSC output.