If Leicester were to win the CL it would blow their league win out the water in terms of how impressive and how much recognition they get for it.
If any team were to retain the CL it would be a much bigger and more impressive achievement than back to back domestic leagues.
This is where i disagree completely. For a club like Leicester (or any other relegation battling club), winning a league means that u must be on average better than your opponent, who is in reality better than you 38 times on average. This is what Leicester did, they beat the odds 5000-1 and won Premier league. This means overachieving for 38 times ahead of bigger better clubs. Entire season!
Now for club like Leicester to win Champions League, it means on worse case scenario doing the same stuff, overcoming the odds and overachieving in 6 group stage games (do not even have to win them all, just enough points to advance) + 7 times in playoffs. Once again u dont have win against your opponents all the time, goal differences, away goals and all that other nonsense comes into play. Put those 2 into perspective and anyone will see that relegation battling squad to win domestic league, ANY domestic league is by far superior achievement than any cup tournament ever will be.
Also look at Leicester luck this season regarding the draw. They ended up in weakest group and had no issues getting pass (so you quite often even do not have to overachieve if the club is from major league) and got a lucky away goal in Sevilla, while being close to bottom of table in Premier.
It is totally different case for squad like Barcelona. The odds of us winning La Liga in recent 10 years have been more or less 50%. We only have 1 (or lately 2) real opponents to worry about, we are just that much better than anyone and it is more or less the case of who chokes less and manages to win El Classicos. CL has alot more random elements involved, the 2-way tie makes it harder, u cannot compensate a bad result (like vs PSG) by winning 10 games in a row, u are out.