Would you guys recommend the solo or normal mode? What is the better story experience?
Yeah, it really comes down to personal preference.
I prefer to play as a single protagonist, putting myself in her shoes as far as possible and trying to make consistent character choices on her behalf: The solo mode suits me much better.
Others prefer to play as observers or puppet masters, putting various characters in lewd situations and watching how they play out in the third person, without getting too involved in any one character. The full story mode is designed for those players.