[theoretical] World Cup Champion vs Champions League Winner

Bayern would currently destroy everyone.

 

If all the best players were from one country, you could argue that the World Champion had a chance, but it's never the case. You could try to argue that Germany right now is the best team because of Bayern, but some of the best players for Bayern are non-German(Robben, Ribery, Alaba, Martinez, Mandzukic,..).

Same with Spain, their National Squad is good but clubs like Barca and Real are dependent on foreign guys like Messi, C. Ronaldo, Ozil, Di Maria, Pepe,...

Your talent pool is somewhat limited if you only have players from your country, while clubs can buy the best XI from all over the world.

The World Champion is basically the best two, three clubs in the country minus some of their absolute stars(Germany: Ribery, Robben, Lewandowski, Alaba, Martinez, Pisczek,... Spain: Messi, Ronaldo, Pepe, Özil, Di Maria, Benzema,...).

Also, the club teams practice daily while the national teams have like 6, 7 games per year and barely practice together, so the chemistry, tactics and automatisms are way better for the club teams.


Regarding your second point about basketball, maybe 90% of the best players in the world are from the same country. USA has all the guys you can dream of when creating a roster, all positions are covered by their respective best players in the world. Basketball is a game of stars. The more you have, the better you are.
That point somewhat leads to the conclusion that the US squad would win vs. the NBA champ, the difference in talent is too big.

NBA: Chalmers/Noel, Allen/Miller, Wade, Bron, Bosh/Andersen

USA: CP3/Deron/Rondo/Kyrie, Wade/Harden/Iggy, KD/George/Melo, Bron/Bosh/Love/Aldridge, Dwight

All these Team USA have high ball iq's and incredible individual skills, which more than makes up for the lack of practicing together and automatisms.