I've been taught both techniques - and they are appropriate for different situations.
If you are doing a PFL (Practice Forced Landing) then you will be using the glide approach. As your approach is steeper, you need more energy to move from the descent to the flare, so the approach speed is higher.
If you are doing a short field landing, you want to be at the minimum safe speed during the approach. In my aircraft, that is achieved on the back side of the drag curve, so high power, low speed, shallow approach.
I'd say that shallower (powered) approaches are easier. You have longer on final to stabilise and the change in attitude to flare isn't significant.
That doesn't make them the right technique to use though!
I actually find flapless landings the easiest, as you have much longer in the flare (higher approach speed) . However you don't want to do them regularly unless you have a very long runway and you don't mind the additional tyre ware (due to the higher touch down speed).
I believe it comes down to the glide ratio of the airplane. For standard GA planes, its probably around 1:10 making a glide angle of around 6 degrees. This means that if you are on a 3 degree glide slope you can't make the runway in the event of an engine failure. For 737s and the like, the glide ratio is more like 1:15 or more. They might not reach the touchdown point, but if on a 3.5 degree glide, they can probably still make the aerodrome (remember a BA flight into Heathrow a couple of years ago?).
So you have to balance the two safety aspects (engine failure vs slightly more difficult touch down), obstacle clearance (often small airfields have obstacles that makes a steeper approach advised), circuit size (again - can you land back on the runway if an engine fails; what are others doing; noise abatement
efficiency (smaller circuit = quicker, especially at busy places). Just because something is difficult, doesn't mean that you shouldn't learn how to do it.
I normally do a slightly steeper glide (probably around 4 degrees) to land at the CAT touchdown point, since I fly from a large airport. This means I'm not diving onto the runway but since there is lots of extra runway to play with, if the donkey dies, I can still land on.
However despite all of that - I'd do what your instructor says to do. Discuss it with him when on the ground. However you would be considerably wiser to trust your instructor than what you read in an anonymous internet forum. Many people on here are
almost certainly experienced pilots and instructors, but the only person that you can be sure is an instructor, is the person sitting beside you in the plane.
If it helps - there have been at least 2 instances of engine failures at my flying club over the years when in the circuit. Because the trained and practised technique is to stay within landing distance when in the circuit - both pilots and aircraft made it to the ground without scratches.