Your 2nd TV is a CRT? Well that would be why, as that TV was designed to accept and properly display a composite signal. The LCD TV has to upscale that input, and some just do a poor job doing so, with too many artifacts. The one you have probably has a bad or nonexistent comb filter. Regardless, Composite video by definition is combining the luma and chroma on the same signal, and this is what causes your issues.
Again the only thing to fix it is to use a different TV, or get an upscaler. Could try a Retrotink Mini (https://www.retrotink.com/product-page/2x-mini) but they are not foolproof. The OSSC probably does a better job (https://videogameperfection.com/prod...can-converter/) but costs a bit more.
You ought to check into something like