I play mainly Eurogames and RPG's - but I approach them in very different ways.
With Eurogames, I play for the strategy and min/maxing opportunities. I don't usually need extravagant themes or components (wooden cubes are just fine by me). Just give me interesting strategic choices and I'm happy.
On the other hand, with RPG's, it's all about the story. I focus mainly on trying to create quality moments through solid character development rather than just trying to play efficiently. It's more about doing things that are consistent with what the character would do rather than just trying to play the best strategy I can.
I'm not all about combat in RPG's. I really enjoy playing out social role-play scenarios and seeing dramatic scenes go in unanticipated directions because of the dice, other player decisions, or both. However, when combat does occur, unlike my indifference to components in Eurogames, I really enjoy fun maps and interesting figures to help visualize the scene. It adds a lot to me if the figures, the terrain, etc., are all as close to what is happening in the story as possible.