waifu2x is not suited for actual anime almost at all - its upscaling is primarily trained on sharp lineart, and lineart in actual anime is generally quite soft.
Anime4K has even less going for it than waifu2x does, it's pretty much just simple warpsharping with a fancy marketing name.
Neither of these are particularly interesting as far as upscaling / remastering goes, and I'm saying that as someone who has done SD to HD anime upscaling/remastering projects from SD masters myself. And while you can get results that look pretty solid for the most part, it is ultimately still going to look like an upscale when compared to native footage. Here's a comparison with two examples:
As you can see in the second example, the upscaled nature of the SD to HD conversion is especially clear in areas where the lineart has been very tightly packed originally.
waifu2x is quite reasonable for manga though; it's quite commonly sharp lineart. I ran it on some old poor-quality jpg scanslations I had, and the results were good.
[1]: https://github.com/bloc97/Anime4K