I don't have a definitive answer, but let me respond with my thoughts on this. I have read a lot of comments on the web with varied results when comparing induction vs radiant cooking elements.There are several variables in play that affect the results people report. The diameter and wattage of the electric coil, whether it is solid disk, ceramic glass with ribbon element, or the older typical coil. The ceramic heats faster and transfers heat better to a flat bottom pan than the other two types, assuming equal wattage and similar diameter the element.
As far as performance of the induction unit, in my opinion, the cookware seems to be the most critical variable. The major variance is the amount and type of ferrous material in the pan bottom. I have both a 1900 watt 7 inch ceramic cooktop element and a Vollrath Mirage 1800 watt induction unit with a 7.5 inch induction coil. I have cooked on both with a 25 year old 3 ply stainless cookware with thin iron ply between two stainless ply. I also have used my new All Clad d5 5 ply cookware(3 layers of stainless and 2 layers of aluminum) on both units. The older cookware boils water slightly faster on the induction unit,whereas the All Clad is even faster. Having said this, I am not talking twice as fast but several minutes faster. The All Clad performs better on both units than the older cookware.
As far as cast iron goes, it will heat slower and cool slower. My Le Crueset dutch oven did beat the electric, but took longer to boil than the stainless. Also not all 1800 watt induction units have the same efficiency.
The thing that impresses me most with the induction unit is how much control I have over the heat. I can go from simmer to boil in seconds and then right back to simmer just as fast. I'm sure you already have experienced this. With 100 levels of control, I can really fine tune the temperature. The new All Clad is so efficient that I don't have to use much heat. I can sear at medium on the electric cooktop and less than 50% on the Vollrath. In fact I pan seared salmon tonight with a nice sizzle at 30% then finished it at 20%. Nice crust on the outside and tender and moist inside.
I hope I didn't bore you with all this. I wouldn't worry about the boiling water comparison until I tried several different magnetic pots/pans from different manufacturers. I would be more interested in how the different cookware performs on the induction unit.