I just bought a used mirrorless camera - Sony A7C if it matters, and and am wanting some advice on a zoom lens.

I want a lens for use in a dark arena - there are dozens of performers with spotlights, so a lot of dark and light. I want to go between shots of the full arena and zooms onto individual acts or performers. I think that my best choice is between the Sony FE 24-240 f/ 3.5-6.3 and the Tamron 28-200 f/2.8-5.6.

Will there be a significant difference in low light performance between these lenses? I like the wider specs of the Sony lens but am not sure how much of a tradeoff I would be making with the smaller aperture.