Muzzle velocity and by extension, impact velocity determines how a bullet will behave when impacting game.
With the mentioned cartridges, launch velocities for the 139-140gr bullets is in the 2,800-3,000fps range.
I've had outstanding success with the mentioned bullets on elk. No experience on Moose... Caribou split the difference in size between the deer and moose.. so can be extrapalated...
I've taken several dozen deer (whitetail and muley) with the 7mm08 with the mentioned bullet weights and a friend used the rifle in '05 to take a large bull elk. The bull was shot 4 times. Three times through the chest (heart/lung) with the Nosler 140gr partition, and a fourth through the shoulders with a 140gr Sierra BTSP (gameking). The only bullet not to completely penetrate was the Sierra which was balled up under the hide on the farside.... Everyone else in the hunting party were carrying some form of "magnum". All were amazed at the performance of the "little" 7. Several attempted to buy the Rem.M7 w/20" bbl which weighs a delightful 7.3lbs with the Leupold Vari-X III 2.5-8x scope.......
However, for body shots on deer, I've found the Nosler 140gr Partition (at least the box I have) to expand too much and not penetrate as much as either the 139gr Hornady, nor the 140gr Remington CorLokt. (facing/angling shots). All the deer I've shot in the body with the Noslers have run over 75yds and involved tracking with minimal blood loss........ I 've also had "problems" with the Hornady 139gr SST failing to expand. The Nosler 140gr BT and Sierra 140gr always expand well and penetrate as well as the Nosler Partiton's in this weight. So, no need for heavier bullets or "trick" bullets in the "little" 7's. They "earned" the 7mm's reputation for game performance by not "over driving" the conventional bullets.
However, that said, I much prefer the 150gr bullets in these cartridges. They perform and behave just like a 180gr bullet from the .30/06. A good recomendation !!!! (I've got "more" experience with the '06, with over 100 deer taken with it, with bullets from 125gr to 180gr, but I'm a "convert" to the 7's..... sort of...)
So, it depends....... Shot placement is always IMPORTANT, regardless of what you're shooting.
FWIW; my brother has always used the 150gr Nosler Part. in his .308wcf (pre-64 Win Mod-70 FW) on everything, and has taken a half-dozen elk along with numerous deer, and a "once-in-a-lifetime Desert Bighorn sheep. All but one elk have fallen, either DRT, or a short run after a single hit. The 7mm08 with the 139-140gr bullets essentially performs like a 165gr bullet from the .30/06- Hence, it will work........
Has for over 100yrs..... The "Magnums" need heavier bullets to compensate for the higher impact velocities......
I know, I have 2, a .257wbyMag, and a .300 Ultra-Mag. These two "need" heavier, and stronger bullets.
Not the 7mm-08 and "company" (7x57, .280, .284wcf, ect). I consider these to be the "perfect" balance for recoil, weight, bore size, ect........ And the little Remington M7, to be the ideal rifle (considering cost..... Not a slam against the Kimber, New UltraLight Arms, ect....).