The .44 may be a little better with lighter weight jacketed expanding bullets.
I have never owned a .45 of any kind, but I have owned several .44 Mag revolvers. I have also fired quite a few .45 Colt revolvers owned by friends.
I think the two cartridges are pretty close to being equivalent when firing bullets in the weight range of 265 gr to 340 gr.
I think the .44 mag may shoot jacketed bullets in the weight range of 200 gr to 240 gr at greater velocities than the .45 Colt. The .44 mag. may enjoy a small advantage in this weight range when expanding jacketed bullets are being used. But many .45 revolvers have been known to shoot 225 gr, 250 gr, and 260 gr bullets quite well.
During the last 25 years, many handgun hunters have adopted the use of heavy for caliber, hard cast, non-expanding, wide flat nosed, bullets fired at 200 to 300 fps lower velocities than is typical for lighter weight jacketed bullets in that caliber. The hard cast bullets depend on their weight and a wide flat meplat to create a load with extreme penetration and a larger than caliber wound channel. In .44 mag, hard cast bullets of this type typically weigh in the range of 300 gr. to 340 gr. In .44 mag, these bullets are typically fired from hunting revolvers with 5" to 8" barrels at velocities ranging from 1050 fps to 1350 fps.
The deep penetration and adequate wound channels provided by heavy hard cast bullets have proven to be very effective on large heavy game with thick skins, massive high density muscles, and large heavy bones. They are also effective on deer, black bear, and elk; although they may be no more effective than the best strongly constructed lighter weight expanding jacketed bullets for this purpose. Recoil with loads using bullets at 300 gr and over can be pretty ferocious in a .44 mag revolver.
Since hard cast bullets are designed to be non-expanding and (pretty much) non-deforming, it would seem that the use of a larger caliber bullet would be one of the few available options for creating a wider wound channel. So for the hunter who favors the use of heavy hard cast bullets at moderate velocities (typically in the 1050 to 1300 fps range), the .45 Colt would seem to enjoy a modest advantage with bullet weights ranging from 300 gr to 360 gr.
Many .45 fans say that the recoil of these heavy bullet loads seems (or feels) less severe (or sharp) with the .45 Colt than with the .44 mag. They also point out that these heavy hard cast bullets don't require maximum velocities to get the job done.
But all of my hunting has been in the lower 48 western states, and I have observed that for game up to and including the size of elk, the best strongly constructed controlled expansion jacketed bullets in the weight range of 240 to 280 gr work quite well when fired at near maximum velocities from a .44 mag revolver. (I generally prefer JSP bullets for anything larger than deer.)
.44 mag loads using wide flat nosed hard cast bullets in the range of 250 gr to 290 gr. also work quite well for close range defense against (black) bears and for hunting larger animals. Hard cast bullets in this weight range still have plenty of penetration and do not require maximum velocities to be effective. Contrary to the beliefs of many hard cast bullet fans, you don't always have to choose the heaviest for caliber bullets to get excellent penetration from WFN hard cast bullets.
My preferred .44 mag load for large mule deer and elk features a 270 gr Gold Dot (now called Deep Curl) JSP at 1300 fps from a 6.5" barrel. Recoil is stout but manageable. This load has been used by many hunters to give excellent penetration (often through and through) on elk and black bear along with modest expansion (often in the range of .46 to .54 on recovered bullets.) These modestly expanding JSP bullets in .44 mag give comparable penetration and the same wider wound channels as WFN hard cast bullets fired from a .45 Colt.
I think this modest expansion from bonded controlled expansion JSP bullets is ideal when compared to the classic double caliber mushroom style expansion delivered by some JHP bullets. Bonded JSP .44 mag bullets (at impact velocities < 1300 fps) kind of flatten out to a diameter of nearly half an inch or sometimes a little more, but under some conditions they may barely expand a few hundredths of an inch (which makes them equivalent to a non expanding .45) Large diameter mushroom style expansion (seen with many JHP bullets) often seems to limit penetration on larger animals at typical revolver velocities.
For this reason, bonded controlled expansion JSP bullets are probably preferable to all but the most strongly constructed JHP bullets (like the Swift A-frame) for use on black bear and big hawgs. Strong bonded JSP bullets and WFN hard cast bullets of the same weight and at approximately the same velocity can be expected to give pretty much equivalent performance and penetration.
Good luck with your large caliber handgun hunting.
