Conditional display of views based on comparing node taxonomy and user taxonomy
First, your view needs to be set up with a display of type "Content Pane". For this to be possible you need to enable the Views Content Panes module which is part of Ctools.

Next, you need to add a contextual filter (also called an argument) for your taxonomy field. The option to do this is under Advanced on the Views UI for the view. The process is similar to adding other parameters to a view, so I'll not cover it in detail.

Once the contextual filter has been added you need to ensure it can be supplied by the panel you are going to add it to. To do that, click on the Edit link next to "Argument input" under Pane settings. Set the source of the argument to be "from context" and the required context to be "term ID of first term".

On the panel editor, you need to add a context for the logged in user. On the contexts tab for the panel, select "user" for the type of context to be added, then press the add context button. Choose suitable identifiers for the user context and select the "logged in user" option, then hit Finish.

Now from the same tab, under Relationships, you should be able to find an option to add a taxonomy context via the user context. It'll be labelled something like "Taxonomy term from User (on User: fieldname [field_fieldname])". Add it and assign it a meaningful identifier.

Now finally you should be able to add your view display pane to the panel. On the content tab, you'll find it under "View Panes" on the add content dialogue. After you click on it you should see the settings for it, which should consist of a selector linking the contextual filter from the view to the context from the panel. If there is only one taxonomy term context available, the correct value will probably be already correctly set. Save everything and test. 

Good luck!