Both can get you in the middle of a addiction.
APAP is gonna be more dangerous, as it is commonly mixed with horrendously low amounts of opiate/opioid drugs, requiring massive heaps (if you don't CWE) of APAP just to get "enough" of the desired effects of your D.O.C.. This can kill you very softly (but very painfully) in a couple of days if you do it good enough. Those liver cells are gonna die ONE-BY-ONE, like a field of tulips sprayed with herbicide. eventually there is nothing left.
Alcohol is less dangerous to your liver simply because of the the lower amount (of actual alcohol) and the rate your body gets rid of it. As if it were apap, the more we consumed could double or triple, even quadruple the half life, because there is more shit clogging up the garbage disposal than it can shred.