If you're looking for modestly priced factory loaded hunting or self-defense ammo for your .44 mag, this American Eagle 240 gr JHP ammo from Federal is worth considering. The designation is AE44A and it's advertised by Federal as suitable for Indoor Range Training. I've found it works well for modest range deer hunting as well. Federal advertises this ammo as having a muzzle velocity of 1230 fps. From my 5" Smith and Wesson 629 it actually averaged 1260 fps.
I did not test the ammo for accuracy over a bench, as I seldom shoot a benched handgun. I did however shoot it on both our police qualification course, from 25 yards to 3 yards, including rapid fire, speed loads, and weak-hand drills. I also shot it at various targets and steel silhouettes to 50 yards. The ammunition performed well, netting me a score of 300 out of 300 points possible. Yes, the shots on the line were a real squeakers! It also shot well on the steel silhouettes at 50 yards from offhand.
Pleased with the accuracy of the ammo, I decided to try a penetration & expansion test, into water-filled one-gallon plastic milk jugs, at 20 yards. The results were impressive. The bullet penetrated into the fourth jug, bursting the first jug, and tearing a great hole through the second. Recovered bullet weight was right at 240 grains, and the expanded bullet measured .665" diameter. This is bargain ammo? For sake of comparison, most defensive type hollow point .45 ACP ammo I've tested penetrates to the third jug, and expands to about .75" diameter.
Armed with the knowledge that this ammo was accurate and that the bullet expanded and penetrated well, I loaded up the 629 and a spare speedloader, then carried it on a couple of scrambles through the Cascades and eventually on a couple of hunting trips. Eventually the opportunity to try this factory ammo on a mule deer doe came up, and I sent two rounds into her chest, at a range of about 20 yards. Sorry, with a handgun in my hands, I usually shoot two or three times, too much of that cop, SWAT & military training I guess. Both bullets smashed through - one through a shoulder blade, the other through the ribs. Both expanded violently, and exited. I'd love to show you a recovered bullet, but they're somewhere in a sage covered hillside.
My conclusion is that this is pretty darned good ammo, likely not the best for defense against large bears. I think penetration is a little lacking for that role, but for deer hunting, even after my limited experience, I'd have to rate it as worthwhile. Frankly, I was pleasantly surprised by both the accuracy, and with how well the bullet itself performed.
Widely available, and not the bargain it once was, it's still affordable. Graf & Sons lists it at $34.59 per box of 50 cartridges. www.grafs.com
You can check out the ballistics and other info regarding this American Eagle .44 mag ammo at: www.federalpremium.com
Normally I load my own .44 ammo, and have for 25 years, but this factory ammo is pretty darned good! Plans are to test this same ammo from a Marlin 1894 rifle as well.