It will depend on the quality of the electronics that you use as well as the portion of the frequency spectrum you are processing (e.g. just bass frequencies or full spectrum).
Personally, I can always tell when a full frequency signal has been run through DSP and have tried high end solutions like the Legacy Wavelet and DEQX, as well as cheaper soluions like MiniDSP. Especially with tube equipment, DSP tends to null a certain sense of breath and decay, resulting in just a slightly more mechanical sound, even if just in the "nth" degree. For this reason, I will always avoid full-frequency DSP moving forward.
I don't mind DSP to improve bass integration and response, say for 150hz and below. I believe DSP is more effective for the bass than a passive crossover as DSP can be more finely tuned, through phasing / time alignment, parametric EQ, crossover slope, etc. where an analog crossover is more limited.
I like the tone of analog crossovers, but have found them harder to integrate, and if they can't be properly integrated, I couldn't care less for them. I currently integrate my subs with DSP, but I run my speakers throught the full frequency. I guess one more step I could take would be to run the signal going to my speakers through a high-pass filter or analog crossover to possibly make for even better efficiency and control, but I haven't felt the impact would be worth adding another step in the chain. Maybe one day I'll try.