I teach on 172SPs and use both techniques. I start with the 'powered' approach because it helps to demonstrate that throttle isn't a 'speed controller'; it is an aircraft control and therefore has a number of interlinked effects.
Trying to steer clear of numbers, most approaches are flown with 1500-1700rpm although the precise figure doesn't actually matter. I sometimes demonstrate landing with this power setting if a student pilot has difficulty understanding what is happing in the flare (speed reducing, AOA increasing) as the technique gives more time in the flare to observe what the aircraft is doing (not good practice on a short runway
)
I tend to stick with powered approaches until the student pilot is achieving a high success rate and then introduce the glide (from downwind). Once these two approaches are sorted, we then discuss how each type of approach has advantages/disadvantages. Both need to be part of a pilot's repertoire although the glide is the more difficult art.
One final point. "Chop(ing)" the throttle is not necessarily a good word to use. Throttle is a variable control and deserves to be treat with some care. I prefer to describe the technique as reducing power or retarding the throttle in a measured fashion. As already stated, there are a number of aerodynamic effects when you change power and good pilots want to carefully balance these effects.
Ultimately, you will become more comfortable with a particular technique (just as most pilots have their favoured x-wind technique). As long as you understand the pitfalls of each and the times where you may need to use an alternative, you will be fine.