For whatever reason, playlists do not have the same degree of customization that a regular library view does. That said, a library view doesn't have the playlist buttons across the top!
I think it boils down to the fact that a playlist is not a view in the truest sense. It is, like the name says, a "play" list/queue, not a standard library view, where you're looking at your entire library organized in a specific customized way. Does that make sense?
In the event you are unaware, middle-click the blank tab bar space (to the right of the tabs) and MC will cycle through the various list styles... Details, Tiles, Thumbnails. To me this is easier than right clicking the tab, selecting list style, and then selecting a specific option from the sub context menu after that. That said, displaying a "playlist" view with panes or categories is not possible - that is limited to only "true" library views.
MC does remember the last list style you chose however (Details, Tiles, Thumbnails) between sessions, so in that sense it customizes the display style. Hope that helps.
