More definition/separation between tracks, more headroom? Or is it just the added 'warmth' you get with analog gear?
Definately all of the above plus hands on control. But Its not something your average person will pick up on, or even care really. But if you are a real nut, you will know the difference, you will FEEL it in your soul and you will get more pleasure out of writing music. I reckon that its easier on the ears too.

But if you don't have the budget, you can do without it.

( feel it in your soul? I talk some real shit sometimes ;) )