Grog and Vax'ildan have an antagonistic but friendly rivalry and often play pranks on each other. Grog, like Vex'ahlia, seems to have little empathy for Vax and Keyleth's growing relationship, and Grog once tried to embarrass Vax in front of Keyleth by pantsing him (but failed).
However, when facing off against Earthbreaker Groon, Vax was one of the people Grog asked to fight alongside him, which suggests that whatever his feelings toward Vax, he at least respects Vax's combat prowess. While visiting Ank'Harel, Vax took it upon himself to look after Grog due to the goliath attracting the attention of the people there. During their time aboard the Drensala Vis, Vax spend time entertaining Grog so he wouldn't be sad without Pike and Scanlan.