I am the same age as you 61 and the answer is yes but.... With respect to hill climbs, the best P/1/2 elite men did the San Bruno Hill Climb this year in 15:XX and the best 55+ 17:XX which by calculation is about a 50 watt differential 380 to 330 watts (climbers). With respect to time trials, the spread on 40K TTs in our State championships is about 5 minutes: 48 minutes to 53 minutes for the men's open to the 60 to 64 age group. At the track, a great flying 200 time is low 12.X for 55+ with the younger sprinters at 10.x. So the hill climb, sprint times and TT data confirms a roll off in performance. However a 53:xx 40 K TT, a 330 watt 3 mile hill climb and 12 second flying 200 meter sprint are excellent performances that few racers achieve at any age.
I started racing in 2007 and I have competed in over 20 road and track races so far this year including two stage races where I am competitive against younger men as well as my peers. I have improved substantially over last year and upgraded to Cat 4 for both road and track. My power numbers are improving across the board with the most gain in sprint power. I am improving and I am competitive with my racing peers which is all that matters to me.
IMO, as one ages, we have to work harder, eat less and weigh less, recover hard and HTFU more than we used to.