Note that a straightforward universal machine for the lambda calculus can be orders of magnitude smaller than for Turing machines [1].
[1] https://gist.github.com/tromp/86b3184f852f65bfb814e3ab0987d8...
[1] https://www.ics.uci.edu/~lopes/teaching/inf212W12/readings/c...
[2] https://compcalc.github.io/public/church/church_calculi_1941...