WordPress Themes and SEO

[cangelmarketer]

I am helping out a client with updating their website. 
The theme they currently have hasn't been updated in ages (I am going to guess years).

Would there be a difference in updating to the most recent version of their theme and changing them to a completely different theme? Or because they update in the current theme is so large anyway, it won't make a difference in terms of SEO.  The reason I ask is that they don't know their Themeforest details to log in and download the most recent version of the theme, so they would have to re-purchase it, and with the hosting, they have access to a range of themes includes in their package.

Thanks