Barcelona in UCL does not have a significant burden because it could be said that group H does not contain strong teams. They can easily qualify from the group phase, but in the future I think Barcelona will have difficulty making progress because Barcelona has many injured players and several players need to restore their rhythm, Barcelona cannot perform much better even in a difficult situation for the squad.
But in the future, Barcelona must have had most of their injured players back on their feet unless they meet up with more karma. I believe they don’t have much stress in the champions league because of the group they’re placed in and the teams that are playing and competing with them in the group stage. Before the end of the group stage matches and qualification for the next round, they must have had most of their injured players back and ready for the knockout stage which is more vigorous than the group stage matches.
In La Liga, maybe it depends on Real Madrid's consistency. If Real Madrid cannot maintain its consistency then Barcelona has the opportunity to compete for the league championship. We know that in La Liga these two teams will definitely be chasing each other to get points, it's true that La Liga is still long but the habit looks like it will continue.
Barcelona have always being known for their good performance in the league even when they’re performing poorly in other competitions. I know the two clubs are rivals and their rivalry will continue for a long time to come. Real Madrid will always play better in the Champions League and Barcelona will always do better in the La Liga matches. With time, we will know who will do better in the long run and have more opportunity of winning any of the titles they’re currently playing in.