Complicated runs, stunning notes and amazing vocals all round are fantastic, but they lose their lustre if you produce an average performance live. Live performances sell the CD version, so they must be top notch otherwise no one will buy the record.
If you find it very difficult to do the entire song without stopping, make it easier and/or let it slide for another track. Do what you are capable of. Always push yourself, but not TOO far otherwise you will sound like an amateur and be known as another vocalist who cannot sing.
Matching and/or outdoing the CD version is possible, but only the most dedicated can do this. Relying on a backing track works for a while, but there will come a time when people question your talent. Soon you will hear “Can she manage without the backing track?” and “I shouldn’t have paid hundreds of dollars to hear the CD live….”