RE: but it's working on all other sites that have not been upgraded
... and I updated CF7 & WP a few days ago on numerous sites on several different servers with absolutely no problems.
You have a problem on one site caused by some issue or issues on that particular site. There is something different of that site. I don't know what it is but I have absolutely no doubt it is there.
Maybe the update of CF7 didn't complete properly. Maybe one of the other plugins on your site created a conflict when you updated WP.
To solve your current problem you will need to work through the issues for your particular configuration.