What's the difference between landing pages and panel pages?
I do not see much difference between both, in fact landing page itself a panel page.The only difference I can say is there might be predefined pages like user profile, node template that we can override using panels and thus making them a panel page while landing page is pretty much same as a node with a url to navigate and contents with various ways might be static text, embedded blocks and much more.

Panels should be never be considered as a tool to build static pages as they are resource intensive,instead use nodes for that purpose.There are many reasons why node is preferred instead of panels like node being entity has attached attributes like author, created time, revisions, also there is long list of node api which allows you to hook into node edit/insert/view processes.