If im correct Kaguya's chakra is much more than Sasuke's and she was drained way before they were even contested in the chakra department.
Sasuke and Naruto never synchronized with her dimensions.
Amenominaka uses up a ton of chakra if it's capable of draining Kaguya. If Obito travels to her dimensions, it'll use up even more chakra since they aren't his dimensions and he'll also be drained much faster than Kaguya due to less chakra as well.
That is unless she wants to stay in the dimension she teleports both Obito and herself to instead of leaving him there. Since that's practically what happened during the Naruto, Sasuke and company vs Kaguya fight.
Everytime Kaguya teleported them and herself, instead of just leaving them, she chose to stay there and try to take back her chakra.
If Kaguya drags Obito to one of her dimensions, Obito might have to synchronize and use his Kamui to travel back to Kaguya who could be in another one of her dimensions which means Obito's chakra will be consumed even more. Her chakra will be consumed as well but Obito's consumption will be greater since the dimensions he's traveling to don't belong to him. Obito also has less chakra in this case so he'll be running low before Kaguya.
If you want Kaguya to try to take back her chakra in this scenario then Obito could actually win. This time, Kaguya will stay in the same dimension Obito is in to try to take back his chakra. In order to do that, she has to make contact with him but Obito also has the seals that require contact and if he touches her with the seals, her power will get sealed away. Not to mention, Kamui's phasing could also prevent that kind of contact. Although if she manages to get her hands on him first, he could get paralized even if it's temporarily.
