Suppose John has 5 sweets. Is there any difference between the following two sentences?
Jack has 3 times as many sweets as John.
Jack has 3 times more sweets than John.
I prefer the first construction and would know unambiguously that Jack has 15 sweets in this case. However in the second construction I would be inclined to think that Jack has 20 sweets, since it seems to suggest 15 sweets in addition to the original 5.