I didn't have the time to complete a thorough evaluation of Busted and LuaUnit but have come to the conclusion that I will use Busted. Both Busted and LuaUnit work well and, given Lua's dynamic nature, I found it easy to write tests with them.
I came to my decision after going back to the Stockfetch tests after a gap of two or three months. It was much easier to work out what was being tested from the Busted tests than it was from the LuaUnit ones. It was because of the names that I had given the tests not any failing on LuaUnit's part.
So my choice was not made on a technical basis but because Busted encourages me to write more understandable tests.
I also found, in some cases, Busted's spies, stubs and mocks made for shorter test code than using Lua's flexibility with LuaUnit. On the other hand, LuaUnit tests seem to run much quicker than Busted's. Around ten times faster in my case.