I seem to prefer live, judging by the time I spend and the number of games I play. Nonetheless, correspondence has its appeal. I played it regularly from the mid-1990s (post cards) through 2018 (websites like chessdotcom the past fifteen years). In correspondence, I often spend many hours over several days on a single move. The research aspect, the effort to find the truth in a position, the quest for near-perfect accuracy all have their appeal. However, sometimes I grow weary of such effort. For more than twenty years, it was nearly always my move in at least one game.
http://chessskill.blogspot.com/2015/06/applied-study.html is a good description of the appeal of correspondence chess.
Why some people prefer daily chess over live?

For me, live chess is more exciting, but I cannot deny that Daily chess has its magic. What do you prefer and why?