We were in Eze in April 2010. I don't recall the distance from the parking area to the village, but it was a combination of paved hills and some staircases. But, you're not done once you get to the village, as there are more hills to climb...steep and winding in places, far more gradual in others. At least within the village you can take breaks along the way by ducking into shops, which you are likely to do anyway. As for difficulty... I'm in pretty good shape and found it a little rough at times (mainly as I'm very sensitive to warm temperatures), but my son who has orthopedic issues handled it like a champ. Here is a picture taken a little more than halfway up inside the village. Note the railing on the left, yet that would require walking on some uneven ground.
We were there on our Med cruise a few years ago - and absolutely loved it!! I remember it being very narrow and cobblestoned, but gradual. I don't remember getting winded at all, but I was enjoying it so much and going slow looking at everything!
We have also been there. It is steep -- I could not do it now with my bad knees. Also we were there when there were about 5 bus loads of people -- some sections got very crowded and it was hard passing each other -- some people going up and others going down.