Is it true that - for example- a bow with a draw length of 32 inches and a draw weight of 60 pounds will have more power than a bow with a lower draw length and the same draw weight?
If so, how significant is this differential in power.

I know there are those with more expertise in the matter and I'm sure they'll chime in. But for a quick answer, you are correct. It's all in the power stroke, more draw length= longer power stroke, overall travel of the string.

In my experience a 1" draw length adjustment on my bows was worth a 9-10 fps arrow speed change. Not sure of the power difference, but that's the speed difference.

Bojackson.com's calculator shows a 5 ft/lb ke difference for that 10fps.

Yes definitely. Larry Wise explains it pretty well in his tuning books. He calls it the force draw curve.
With the longer DL, more energy is required to draw the bow back, so more energy is stored. The more energy you put in the more you get out.

Just remember accuracy is the most important thing . It doesnt matter how fast or how hard you are hitting if you cant hit what you are aiming at. In my experiance I have found that anything that shoots over 270 is fast enough. I recently baught a BowTec Patriot it was shooting 320 in a longer draw but I was having accuracy problems so I shortened my draw the accuracy came back and my speed went down to about 307 its still realy fast but now accurate too.

I had a friend of mine that was gonna shoot a hog with like a 24 inch draw at around 45 lbs. I convinced him that he needed to get a bow that fit or he would just wound it... i didnt know it was that big of a difference though.
Thanks for the feedback.

Although a 45 lb 24" bow will kill a hog, it is notthe ideal setup. You would have to have an extremely sharp cut on contact head, a heavy arrow,and you would be severely limited in your shots.

Work is defined as a force applied over a certain distance. Thelonger distance a force is applied over, the more work being done to the arrow which results in more kinetic energy of the arrow.
Having said that, the variation from bow to bow also factors in here. Its possibe to have a bow with a 29" draw shoot an arrow with morevelocity (resulting in greater KE) than a bow with a 30" draw because of thedifference in the dynamics of the bows.One bow may be able to convert more energy to the arrow under the same draw weight...lots of factors here.
But...yes, given the same bow, a longer draw will indeed yeild more energy to the arrow.