I don't think you can make a judgement based on your own experience. Especially since "playing basketball" can mean many things, with the most popular forms not even using a full-court or even using a shot-clock or time limit to get across half-court. I've encountered different levels of exhaustion playing basketball, half-court, pick-up, indoors, with a shot clock, etc. I was extremely exhausted just sprinting up and down on a 35 second clock, after being well-conditioned for full-court games without a shot clock.Certainly my experience wouldn't translate to the NBA or NHL, but from experience I exhausted much more energy per shift playing hockey than I did playing basketball. Again that was a throwaway statement though not meant to be taken too seriously, probably should have just left it out considering it didn't really have anything to do with correcting the mistakes of that other poster.
No other hockey league compares to the NHL either in the same way as your example.
Going back to just the injury itself, an Achilles injury will dramatically effect your ability to jump and land, which are extremely important in basketball.