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Here's my shortest answer (so far)…

def compareTriplets(a, b):
    return (list(map(sum, zip(*(
      (1, 0) if i > j else (0, 1)
      for i, j in zip(a, b) if i != j))))
      or [0, 0])

Also short, but done without for loop…

def compareTriplets(a, b):
    return list(map(sum, zip(*(map(lambda i:
        (1, 0) if i[0] > i[1] else (0, 1) if i[0] < i[1] else (0, 0),
        zip(a, b))))))

I'm not sure whether the for in a sequence comprehension is really considered to be the same as a for-loop, but I thought I'd try to make a solution without that keyword anyway.

Yesterday, I had submitted this longer answer because I was sleepy…

def compareTriplets(a, b):
    at = bt = 0
    for i in range(3):
      if a[i] > b[i]:
        at += 1
      if b[i] > a[i]:
        bt += 1
    return [at, bt]