To me, the ability to dial it in to sound either very "effected" or very realistic. Complete control over the length of the trail. Most of all, pristine sound quality.
I'm not an audio engineer so it's hard for me to be much more explicit than that – maybe an example might help? I enjoy the sound produced by some recent Lexicon rack equiment I've tried, but was frustrated that unless they were presented with a buffered signal they turned to mud. The TC Nova solved that problem and is in pedal format, but to my ears doesn't sound at all close the the Lexicon.
I don't yet have experience with Eventide 'verbs to help the comparison, sorry!