Strictly speaking, Matroska (MKV) is a different container format. It supports chapters and metadata, which mpeg-ts does not. It of course losslessly preserves the original content of the disc. It has very wide, but not universal, support.
MKV is much more flexible than TS, and is more flexible than any other format, in my opinion. Pretty much the only thing it doesn't do is preserve interactive DVD menus (which I don't want, and if you do you can use IFO for that). You should read up on it. It also has useful features like Ordered Chapters, and other such things.
MakeMKV will put each Title from your disc in a different file. You can select which audio and subtitle tracks you want included, and change their name or other parameters at rip time.
Also look at MKV Toolnix GUI. This is a graphical front end to various MKV utilities, that allows you to do things like edit chapter information, and losslessly remux/split/combine video files (including, for example adjusting the A/V sync).
Have fun...