"1 watt of electricity produces 3.412 British Thermal Unit (BTU) of heat per hour regardless of light type incandescent, HPS, CDL, LED, fluorescent, induction, etc. Therefore, a 1,000W HPS grow light (1,060W with ballast loss) generates 3,617 BTU per hour heat"
The hps will output heat just like an LED. LEDs heat mostly goes out of the back of the LEDs and lacks infrared heat so there's that. Also If you use a cooltube on HPS you are getting less light because the glass acts like a screen and I think you lose about 30% going off the top of my head
1000w of led will be the same heat output as 1000w of HPS. The difference is the efficiency of the light especially over time.
Hps requires bulb changes so take that into account when comparing. High quality LEDs will last a long time and will most likely need a driver change before a board goes bad