I wonder if there are any bases like this built for bigger ships like frigates and destroyers. It would be amazing to see a bunker for an aircraft carrier - of course it would require a big cliff next to the sea and some big doors

I did not know about Brest, do you have any photo links?
( I am assuming it is much bigger than the Swedish one with space for 25 submarines)
Muskö were built for frigates and destroyers, its just that the swedish navy does´nt have those kind of ships today (the largest dock is 350 metres long).
I would assume Muskö is much bigger then the Brest submarine pen. It´s not just the docks that are underground, the whole navalbase is built under a mountain. There are repairfactories, hospitals, diningrooms, barracks etc, all under the mountain. Thousands of soldiers would serve there in wartime and the hospital alone has over 1000 beds IIRC. As a comparison, when building the famous underground facilities in Cheyenne Mountains they had to remove 350.000 m3 of stone, in Muskö they had to blow away 1.500.000 m3 of stone (even more if you counting the underground road that leads to Muskö under the seabed).
I thought Brest just was concrete bunkers for the sub pens built by the germans during WW2. Nothing underground about it.
In Norway you have a miniature Muskö outside of Bergen that is still active, it can also hold destroyers.
BTW: I started the Muskö-thread in another forum, you can see the pics and facts in this link;
http://www.militaryphotos.net/forums/showthread.php?t=65025&highlight=musk%F6