It depends a lot because "simple" and "complex" can be a thousand things. For example, a purely semantic system would be easier to adapt to unrelated languages with wildly different phonologies - because it doesn't refer to the phonology at all.
But if by simple/complex you're talking about the number of basic symbols, I guess ~5k phonemes would make the alphabet as complex as a logographic system. But by then perhaps the best solution is neither, it's a featural writing system.