Both are correct, but incorrectly used interchangeably.
10 to the dozen means "very many" (i.e. "a lot of things") e.g. "babies are ugly ten to the dozen", meaning a lot of babies are ugly (but not mine).
19 to the dozen means "very fast" (i.e. "a lot of speed") e.g. "my heart was beating 19 to the dozen", meaning my heart was beating a lot.
The confusion comes about when a lot (of speed) gets mixed up with a lot (of things), resulting in the wrong phrase being uttered: "my heart was beating 10 to the dozen" (i.e. a heart attack).