The Netflix Cowboy Bebop is a good example of how something can be reasonably faithful, and clearly expensive to make, and still fail hard.
They go to great lengths to replicate the costuming, mecha designs, and atmosphere of the original, and they keep the soundtrack, which is one of the all-time great anime soundtracks.
But the costumes look like cosplay, the lighting makes everything look cheap, the depth of field effects and color balance of the CGI makes it look like model shots and not match the live action bits, and the sound mix is off, so the soundtrack sounds muted and tinny instead of kicking things up to 11 like it does in the anime.
Also Spike is suddenly Asian, and Faye suddenly isn't. Also, Faye is basically Girl Spike now, when she was her own character in the anime.
Pro Tip: if you haven't watched the original anime, you need to. Even if you don't like anime, you will probably like this. It has a great English dub, arguably as good or better than the Japanese, so you won't have to read subtitles. Great music, great animation, and just a whole lot of fun.