Is there a noticeable difference in speed (e.g., pingdom tests) in Sydney Pro vs. Sydney?
Both themes are written on similar code base. The only difference on the pro version is addition some extra features which is documented here https://athemes.com/theme/sydney-pro/. Though there are significance difference on amount of code on the pro version, it can’t be a single parameter to determine the site’s performance. But, it is more about how you setup your site and the content that your site loads. There are some actions you should take to improve your site’s performance as explained on the WordPress codex.
I hope this clarifies things a bit.