As someone having just graduaded from crippling anxiety to only being moderately stressed I find that the only difference between those two states of mind is the lack of the previous negative emotion. It's not like I gained a new emotion or my existing ones somehow evolved. It's more like you have pain and then wake up one morning and no longer do. Everything else is the same - just no more pain.
When asked about what does success feel like a person replied that it feels like a relief. I think that's pretty accurate.