If you want to check just a single person, click their avatar and that will take you to their full profile.
On the left side of that page you will find 'performance vs.'.
If you want to see a list of your performance in every game you have ever played, click the little house icon at the top of the page, then find at the top of that page a link to 'my performance'. That will show every opponent you have ever played and give stats.
The only problem with the 'my performance' table is that there are several pages of players, and also several columns of data. As you move down the page and keep going past the first page, the header at the top of the page scrolls off the page and with that many columns of data that are only numbers, you tend to lose track of what each column is for.
It would be nice to freeze that identification header in place at the top of the page and then just let the data scroll up.