To me it's a tie between these two: wide-toothed comb (for my thick hair) definitely does the job more quickly but finger-detangling is safer and less hairs are pulled, even though I'd need an eternity to detangle all the knots considering I spend 15 sec. for each bang.
My method is to detangle with fingers first, then finish using a wide-toothed comb or brush. The best way to do it is in stages - start by combing from the bottom up, in sections of 6 inches or so. If you try going all the way from the top down, you will get so snagged up that you might not get the comb out again.
It's fair comment too that we are the same as our animal siblings that moult. Do not try to avoid pulling strands out as new ones will grow in. I must lose in excess of 200 strands every day and I have successfully maintained a 24 inch mane now for over five years.
Good luck!
RM
My experience: Wet hair -- wide tooth comb, the kind designed for detangling.
Dry hair -- fingers.
What works for me ---- I have curly hair past my shoulders. When I get out of the shower, I spray leave in conditioner in my hair, use a wide tooth comb - start at the bottom/work up. The comb slide thru effortlessly with the leave in conditioner. I crunch the hair/let dry and leave alone.
Bob