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Why on earth would it matter if they use combustion or electricity? Internal combustion engines are pretty efficient. They're not as efficient as electric engines but the amount of energy burned is well within an order of magnitude.

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Electric engines can easily be above 90% efficiency. ICE's are around a third of that -- since they're Heat Engines, Carnot's Theorem even gives a theoretical maximum efficiency.

So yes, an ICE will have an order of magnitude more waste heat. That's why a car engine requires liquid cooling to avoid destruction but a similarly powerful electric motor only has a small fan to keep air running over the windings.

I'm not sure how good a model a heat engine provides for internal combustion. A heat engine assumes a fixed "working fluid" operating between heat reservoirs. In an internal combustion engine, there isn't strictly a "working fluid", since air and fuel are continually added, and exhaust vented away, and combustion adds energy without providing exactly a "heat reservoir".

Why are you talking about waste heat only? Work energy degrades to heat too. The total amount of heat created is equal to the total energy used by the system. ICEs need three times as much energy to do the same work, so they output three times as much heat. This would be true even if electrical engines had 100% efficiency.

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