Close. You left out "resistance" I think. One watt of resistance will create the same amount of heat no matter the source/circuit. In an electric light, watts turn into photons (light) and heat. The better the light is at turning watts into photons (efficiency), the less heat it will produce per watt consumed. A 30% efficient light will turn 70% of its power into heat, but a 50% efficient light will only convert 50% of those watts into heat.
More efficient lights produce less heat, period. They are not all the same.
I would agree generally about "cheap" LED. Cheap generic COBs aren't much more efficient than CFLs and HPS. But even cheap generic Chinese COBs will replace 200w of HID and grow better bud over the given canopy area, without light movers or 12 inches of vertical profile to devote to hanging a reflector. That matters for a lot of 200w cabinet growers. Cheap white 50w COBs are about $1 on Ebay, drivers are less than 20 cents/watt. But cheap is cheap, whether COBs or HID.
Here's the basic efficiency ranges of different lamp techs:
Incandescents: 17 lumens/watt
Mercury vapor: 45-50 lumens/watt
Fluorescents: 60-70 lumens/watt
Metal halide: 90 lumens/watt
High pressure sodium: 107 lumens/watt
Lose cheap as the first priority and the efficiency gap widens dramatically between HPS and LED. The Samsung chips in SolStrips have efficiencies in the range of 187-212 lumens/watt depending on how hard they are driven. That's close to 2x the efficiency of HPS. Add the fact that all the light produced by an LED is emitted in a 120 degree cone aimed directly at the canopy, rather than a 360 degree sphere where 2/3 of the photons have to be reflected back and through the bulb before they get the chance to hit a leaf, and the efficiencies of LED over HID start to become clear, especially compared to smaller wattage HID.
Bottom line, with modern, better quality LED, you use far less watts to produce the same amount of light-on-leaves than HID, and you use those watts twice as efficiently. Less watts total equals less heat, and watts used far more efficiently equals far less waste heat.
Photon for photon, LEDs create far less waste heat than HID, hands down. It's not even close.