Many bands face this question when recording... Record an album that accurately reflects the band's live show, or do a bunch of stuff that can't be replicated on stage?
One plus in your column as a solo artist... you don't really need to worry about this one. Why? Because if you announce your performances as "solo performances", no one is going to expect the performance to sound like the recording! In fact, they are probably looking for that intimate, stripped down feeling.
So as a solo artist, your only concern should be if you can play the songs live so that the song still comes across as something special. Making sure your songs are great goes a long way towards this!
For the studio, you should be thinking about other things. Namely, what are your goals with the recording? Maybe a simple, acoustic album is the right thing for you. Maybe you want to keep that overall vibe, but go for adding more dimension with more instruments and arrangement depth. Maybe you are looking for something more slick and polished...
My suggestion is, where budget allows, make a recording for the artist you *want to be*!
It is a crowded musical field out there, Do everything you can to illustrate why you are special and deserving as an artist. Maybe that is truly best brought out in a simple recording, or maybe additional instruments and a unique arrangement will really bring what you have to offer to the table for your current and new fans!
When I do my initial consultation with an artist, this is one of the big questions I discuss. What do you want to sound like, and what are your goals?
But don’t worry what that live performance looks and sounds like. Your fans know you are a solo act, and they’ll enjoy whatever show you give them, whether an acoustic performance in a small venue, or a full-to-the-wall performance with all the bells and whistles! In fact, whatever you do, bring something to the performance that ISN’T on the record, do it well, and watch your fans start buzzing! Lady Gaga has no problem reinventing her songs at each performance, so why should you?