Why would you not consider the fact that the same team were not as impressive in the league? Any proper reasoning? On the other hand, Barca absolutely dominated every competition they played. It was sort of guaranteed that they would dominate any game and create more chances. Teams dominating them was abnormal. Whereas Real could not even dominate Liverpool before the Salah going off.
I think the main reasoning is that Real Madrid were quite good in La Liga.
In 2013-2014 they finished 3rd in the league, 3 points behind Atletico and tied in points with Barcelona. They also won the Copa del Rey and the Champions League. I don't have a problem saying that, overall, they were the best team in Spain that season, even if they finished 3rd. The league 'difference' is 1 game out of 38 with Atletico and head-to-head against Barcelona (who they beat in the CdR final).
In 2014-2015 they began amazingly well, but injuries derailed their season starting from early 2015, and they ended up losing their sizeable advantage over Barcelona. Without those injuries (especially Modric, who was out a big chunk of the season), Barcelona wins the CL and CdR but I don't know that they're able to catch up in La Liga (they finished 2 points ahead of RM, although drew their last meaningless game, so it's really more like 4 points).
After that, they fired Ancelotti and their bad form continued for the rest of 2015, which seemingly killed their league campaign. However, they fired Benitez and hired Zidane in 2016, and their performances improved. They ended up coming close to catching up to Barcelona, who had their own collapse, but finished 1 point behind them. Zidane technically got more points than Luis Enrique during the period of the season he managed.
So over three seasons you have a three point difference between RM and Barcelona (but really five). Then in 2016-2017 RM won La Liga with a three-point margin. So over four seasons the difference between them is tiny.
It was really only Zidane's last season in which they underperformed. They were not great in La Liga and finished miles behind Barcelona, and were not great in the CL but managed the narrow victories they needed.
Luck always plays a part, even in long samples like these, since titles end up depending on small margins. Real Madrid had a bad calendar year (2015), which cost them two league titles; if they'd had a bad football year (August to May) maybe they only lose 1 league title. Maybe they finish with 3 CLs instead of 4 and 2 Ligas instead of 1. If Barcelona don't have an inexplicable run of terrible form in 2016, they don't crash out of the CL and they, not RM, win two in a row. Or if their inexplicable run of bad form extends for 1 more game, they lose the league title too and RM do a league-CL double in Zidane's first half-season of management. Little details like that.
We can probably say that the MSN Barcelona deserved a little more international success and the BBC RM deserved a little more domestic success. Maybe the 'fair' trophy distribution looks different, but luck and random events play a part too.
On the other hand, Barca absolutely dominated every competition they played. It was sort of guaranteed that they would dominate any game and create more chances. Teams dominating them was abnormal.
Let me make an additional point: comparison between Pep's Barcelona and 4CL RM in the CL.
Barcelona:
2008-2009: 8 wins. 3 wins in knockout stage. (won title)
2009-2010: 6 wins. 3 wins in knockout stage.
2010-2011: 9 wins. 5 wins in knockout stage. (won title)
2011-2012: 8 wins. 3 wins in knockout stage.
Compare to Real Madrid:
2013-2014: 11 wins. 6 wins in knockout stage. (won title)
2014-2015: 8 wins. 2 wins in knockout stage.
2015-2016: 9 wins. 5 wins in knockout stage. (won title)
2016-2017: 9 wins. 6 wins in knockout stage. (won title)
2017-2018: 9 wins. 5 wins in knockout stage. (won title)
Although Barcelona did well in the CL (2 wins in 4 is excellent), their incredible dominance in play did not translate to overwhelming victory, for whatever reason. Real Madrid were not as "dominant" in play but they were apparently better at winning games, and therefore ties.