I've used the 3 most popular 240 JHP's (Sierra, Speer and Hornady XTP) and prefer any of them to the 300's for whitetails. I actually found the Sierra to be the most accurate in most of my .44's, and have therefore used it the most. On some, the expanded bullet has been found just under the hide on the off-side, on others Ive gotten complete penetration. On one, the bullet entered the chest and was recovered at the root of the tail.
The bullet that I use in my 10" .44 Contender is the Speer 200 gr. jacketed magnum hollowpont @ 1600 fps. I've never recovered a bullet, but exit holes are typically 2 1/2".
I'd have to say that any .44 JHP will kill deer well.