Power is rated at 144 hp and 139 lb-ft of torque. That puts it right in the thick of the competition, up on the Honda HR-V but down a little on the CX-3 and down 16 hp and 45 lb-ft on the Fiat 500X/Jeep Renegade twins. A turbocharger may have been a nice add for the C-HR, but the naturally aspirated engine does get the C-HR up and moving in quick fashion, perfect for squeezing through gaps in rush-hour traffic and the like.
See, that's where I dislike peak numbers. I had a 132hp/128lb-ft Corolla, weighing around the same as my current Mazda3 with 148hp/135lb-ft. While the Mazda feels slightly more spritely from 0-30km/h, I actually felt that the Corolla was faster with rural road passing.
Granted, the 2015 Corolla tested back to back with my old 2010 Corolla showed that the 2010 was faster (it's certainly lighter, and the CVT probably doesn't help much); that said, I wouldn't look to peak power figures to determine whether a car is faster or slower.
...and as for the FCA twins, the engine is a dog, strained and moaning away as it lugs around a ton of weight and delivering less than stellar fuel economy. I'd hardly look to it as competition.
If you aren’t going to give us AWD, then at least go whole-hog-hatch-on-stilts and give us a manual option to really get that feeling. You still have the looks, the generous front seat space and good view out (well, forward and out), but with a nice slick-shifting manual box (Could the version found in the RWD 86 work here? Not sure.)
I'd actually think that the base model Corolla powertrain would be the one you're thinking of, since the GT86 uses the boxer engine co-developed with Subaru...totally different dimensions, whereas the transverse mounted engine used in the Corolla (on which the CH-R's platform is based) would be more similar.