No, they have nothing to do with each other.
Example: In the last, Naruto fell victim to the Genjutsu, but Sakura resisted it.
Is Sakura stronger than him, or her chakra bigger than him?
- SM user takes the natural energy, not "chakra" in itself. Had your analysis been accurate, then Kabuto wouldn't have needed to close his eyes. And he did get effected by both the Izanami AND the Genjutsu itachi did to him after that to undo the ET.
No.
1 - The entire team was caught the by genjutsu in "The Last". Unlike Sakura,who used her skills to defeat it, Naruto never tried to defeat it. Instead he left his genjutus and entered Hinata's genjutsu. The genjutsu trap was designed to work that way so for Naruto to be able to leave his genjutsu and enter's another person's genjutsu proves he is skilled in genjutsu. That's very similar to what Itachi and Sasuke did to each other to defeat Kabuto's sound genjutsu.
2 - I know how SM works. The user uses Natural energy, physical energy, and spiritual energy to create sage chakra. While they are using senjutsu chakra they are not using their normal chakra. It's recovering. Pa frog stated confirmed that -
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. That means when a SM user is in SM they have access to 2 different chakras.
3 - Nobody is immune to genjutsu. I never said SM make you immune to genjutsu. Kabuto closed his eyes so he wouldn't have deal with sight genjutsu. Kabuto just learned sage mode not long before he fought Itachi. He may have mastered at SM transformation, but that doesn't automatically make him a master at SM.