I usually don't transcode Blu-rays, I only use MakeMKV to put the audio and video in a different container (mkv). The whole point of Blu-ray is to get the best picture quality, that's why I don't transcode them.
EDIT: that said, mkvs created by MakeMKV will probably not work on your tv, unless you connect your PC to it of course.
MP4, like mkv, is a container format. So the quality depends on the video encoding. I use Handbrakes "High quality" setting for transcoding DVDs. With this I get 99 % of the original picture quality but at maybe 20 % of the size.
If you put the same video and audio in an mkv file and an MP4 file, I believe they will look the same. I mostly use mkv because it is better at handling several audio and subtitle tracks. If you don't need that you probably should use MP4.