Luis is a good and wily player. I like Monreal better for the Alba back up role for say 2 years, but either one would be good quality and smarts where we would not lose quite so much in our overall approach and coherence by letting Alba get some rest.
Nacho Monreal is not a better player than Filipe Luís. Defensively nor offensively. Monreal is decent but Luís would be the better option. He was called up for Brazil last summer during the World Cup and made an appearance. Late last season he broke his fibula in his left leg and recovered after being out for only 2 months. Very impressive. Played great against Juve a few days ago as well.
We are talking about a left back that has been one of the best left backs in the world during his Atlético stint. He is not in his prime any longer but there is no doubt that he could be a backup for Alba for 1-2 seasons.
I would certainly take Luís over Monreal. There is only 6 months between them.
There is a reason why Monreal has been in the periphery for the national team (did not take part in the Euro win back in 2008, the World Cup win 2 years later or the Euro win in 2012) and that he has played for Arsenal since his move there in January 2013.
Filipe is currently the better player and has a bigger role (more playing time) for the much better club (Atlético) while facing much better competition in Lucas Hernández than Monreal has in Arsenal. It is a no brainer for me.
Another thing, Luís is pretty tall for a LB (1.82) and I think that he could play as a CB in rare emergencies. Monreal does not provide this added option.