While it seems that there is no difference in semantics (but I'm still waiting for answers here), there seems to be a small but consistent difference in performance.
\the consists of 4 characters and
\number of 7, so you can type it almost twice as fast! ;-)
\the\numexpr seems to be 10 - 15% faster than
\number\numexpr. As it's not absolutely trivial to measure this, this is how I did it.
profiler library on these three loops:
... in the hope that subtracting the execution time of L3 from L1 (L2) gives me the time actually spent in
(L1-L3) / (L2-L3) then yields about 85 - 90%.
To get a rough feel for the actual speed: a million repetitions of
\the\numexpr takes about a second on my computer.