MakeMKV doesn't convert the video, it's the same as on the disc all it does is pull the video off the disc and dump it in an mkv container.
Most encoders out there use x264 pretty much the best image quality H.264 encoder out there.
Handbrake is one of the most straightforward to get going, plus relatively easy to use but only does limited releases, like 1-2 in a year if that. It supports most media types and generally gives decent video output, it also handles DVD's the best and does cropping a lot easier than most other encoders though cropping black borders isn't necessary with x264.
The downside to Handbrake is you can run into media types occasionally it cant handle, it has poor subtitle management and it's a tad slower than other encoders at similar settings at least in my experience.
BDtoAVCHD is meant for converting Blu-ray's only, it is easy to install and quick to queue up jobs, fast and stable, currently my favourite pick for BD's. Despite the name you can output to mkv with it and it also does 3D Blu-ray's too however you must feed it the raw BD folder structure to get 3D prompts, feeding MKV only works for 2D video.
Ripbot264 supports more media types that Handbrake cannot handle, it is also more cutting edge using the latest versions of x264, can distribute encoding over the network to multiple PC's & is constantly updated. Downside to Ripbot264 is it does take a bit of work to set up and install and time to queue up jobs.
TX264 is a little interesting it's slightly more technical than Ripbo264 & doesn't have all the same features but is a bit easier to get up and running, TX264 exposes
various presets of x264 that can tune for film, animation and squeeze even more quality out of an encode or sacrifice it for speed instead. It also uses the latest versions of x264.
Hybrid, a super technical x264 encoder, exposes tons of options you can tweak.
IVI Pro, a commercial Mac based front end to Handbrake, Handbrake is already available for Mac's & free but this application has one thing going for it in that it auto integrates iTunes metadata into the mp4 videos it outputs so you see the coverart/movie info in iTunes and on your iOS device.
DVDFab Ripper, this is a decrypt-er and encoder rolled into one, as a basic encoder is gives you very few options. It does support hardware encoders though like Intels quick sync which can cut down conversion time by a significant amount, quality wise not as good as x264 but not as bad as GPU encoders.
I'm using BDtoAVCHD to compress my Blu-ray's, works out well enough for me. Use High profile, medium, flim, constant rate factor at 18 and it cuts most BD's in half while looking almost identical to the original.