Just swapped an old and half worn High Roller II off the back of the AM bike and fitted a Minion DHF I had knocking about and it is like night and day.
All the steep muddy slithery stuff I used to struggle to control speed on is now a piece of piss. I think the old tyre was good schooling, but it really helps to be able to get braking when you need it, in shorter burst, rather than madly dragging the back brake and ploughing down in the hope of getting speed right.
So in summary, tyres can and do make a massive difference. Tyres and technique. Tyres, technique and a lazer cock.