I learnt to fly, using power for RoD and attitude for IAS on the approach.
By the time I was instructing, CFS wanted us to use "Point and Power" (ie use attitude to control flight path, and control speed with power) for the Flying Schol cadets. They were paying, so ok!
It works surprisingly well, but as we all know IAS and RoD are a result of the combination of power and attitude, so both methods are just ways to avoid confusing the stude anyway!
On some a/c, though, one method is definitely better than the other. For example, the Katana has an extreme change of lift with attitude change (high aspect ratio wing), so point and power is better, as you get too much of a lift change if you pitch for IAS, (that DROP when you pitch down for an extra 5 knots got my attention every time). I'm sure other contributors will have examples of a/c which are better flown on power=RoD, Att=IAS.