Not really. The luaTeX engine is the slowest and some of its defaults differ from the behavior of pdfTeX and XeTeX. I generally recommend people use XeTeX (which is also slower than pdfTeX but faster than luaTeX), unless either they specifically need some luaTeX facility or they are required to use pdfTeX (some publishers insist on pdfTeX, although their number is declining. I think that arxiv used to (maybe still does) be one site that only supported pdfTeX, but I could be wrong about that.

There are two main TeX distros: TeX Live and MikTeX. Both of them ship the binaries for pdfTeX, XeTeX, and LuaTeX. All three binaries (“engines”) have their users. There are also some other binaries (very few users use “plain”/“Knuth” TeX, and mostly Japanese users use euptex etc).

BTW, unlike the sibling comment I've never found LuaTeX's speed to be a problem: AFAIK it's only a tiny bit slower when loading fonts, but for typical real-life documents the bulk of the time is spent in LaTeX/package macro expansion, where, in principle with enough effort, LuaTeX features could actually considerably speed up compilation, e.g. eliminate need for multiple passes writing to an aux file, for things like table of contents that could just as well be inserted later. (Personally I think it would be nice if everyone used LuaTeX or any other approach that reduced macro hell, but it will be a while before that happens.)