The competition between Barcelona and Real Madrid will be even more competitive next season because both teams have made several efforts to bring in a number of players so that the fight for the La Liga title will be even tighter. Real Madrid will try to make several adjustments with their new coach while Barcelona will be much more solid because they are already well connected with the coach. La Liga next season will still be about rivalry and I am sure that both teams will compete for the title because if you look at it, there is no other team that might be able to match them in terms of fighting for the title.
Barcelona depends too much on Yamal in big matches and while he is very talented and has great ability to make big differences, his living style is very risky for his career. He has close friendship with Neymar who is famous with his uncontrollable living style that is not good for professional football players. Yamal in early years of his career already had some dramas related to his vaccations with a lot of girls around him. If Yamal can not control himself well and let his living style affects his fitness and performances, Barcelona will be affected very negatively.
Of the two teams you mentioned, I still think that Real Madrid will still have a little difficulty when they meet Barcelona again. Because the Real Madrid team still has to make adjustments with the tactics of their new coach for next season, while Barcelona already has quite extraordinary abilities plus new players who can help strengthen all lines in the team. So of the two teams, Barcelona might still be superior to Real Madrid because Alonso still has to make improvements to several players who are currently at Real Madrid.
Real Madrid are preparing for the new season with new players coming to Bernabeu, and they will not easily accept failure against Barcelona in La Liga and even in Champions League. Xabi Alonso is a good head coach but a first season at a new club is always challenging for any coach. The adaptation of Xabi Alonso with Real Madrid as a head coach, no longer as a star player as how he played many years for this club, will contribute to general title race situation between Real Madrid and Barcelona.
Two giants in Spain will have quite fair beginning in a next season and we won't be able to see big point difference between them too soon. Their title race will need several months to have considerable point gap in between and I am still thinking of a revenge from Real Madrid in a new season.