The record of the previous meeting is actually not too important in the upcoming match, but usually the team that is dominant in winning the match is the one who wins it the most. So I think Barcelona are the favorites in that match based on their head-to-head record, but I don't think Barcelona can be completely relied on in Europe this season after they failed in the Champions League.
Head-to-head record is from the past when they had different players and coaches as well as different forms. Their coming meeting will happen with new players, new coaches and their newest forms. Barcelona still have more players who can play creatively and create chances in the match but in Manchester United, I can only see Bruno Fernandez is a player who can contribute creativeness for their attacking.
If Bruno can not play well, Manchester United will lose more than half of their attacking power. With Barcelona midfielders, they can block Bruno and take advantage to win.
This season, Barcelona has had pretty good results in La-Liga, despite difficulties in European competition. However, MU position is worse, both in Europe and in the EPL (now look like better). This is then makes me believe if Barcelona has a better chance of winning than MU in the upcoming match. H2H is superior to Barcelona, but that's not what I see, but the current performance. However, an H2H that is not matched by the current good form will be history.
It's because their quality is not good enough to compete with biggest clubs in Europe. In addition, La Liga has its common tactics that is used by most of clubs in Spain and the league while in Champions League, Barcelona had to play with many clubs from different nations and leagues with tactics they are not familiar with. If they had troubles to win non big clubs in Champions League, they surely get more problems to play against big clubs in Europe.