The original posters question was a valid inquiry.
Though this issue has been 'cussed and discussed often on this and other forums, his question was actually one of the better ones and deserved a reasonable anwser.
I asked the question once as a rhetorical one and got conflicting answers myself.(long before the days of the internet, however). Unlike the majority, I was in a position to "need" to know for valid reasons. Hence, I set about to "find out". I did so by trying the options available.
As a conservation officer, I often had the function to dispatch injured or nuisance wildlife and as time wore on, due to "people" issues, needed to do it in a more "discreet" manner than torching off a .300RemUltMag to put down a 75lb doe caught in a barbwire fence near a community playground, or one that was bleating incessantly at the scene of an automobile accident it had caused; and 20-30 bystanders and rescue workers were compounding the situation.
The reality came to light after I was called because a deputy who was not such a good shot, fired 7rds from his 9mm into an injured doe that proceeded to jump up and run across two lanes of an interstate highway and run in front of another car causing ANOTHER ACCIDENT !! All the while, a superior court judge and county commissioner looked on! (there had been a "stink" about the deputies going to the 9mm. This poured "gas" on the fire !!! But it really was an ammo issue. This got that resolved !!!) Needless to say the single shot from a "Hunter Ed" gun..... a single shot Stevens .22lr (I had it in the truck because I'd just left a Hunter Ed course I'd taught and couldn't get to the .22Hornet) of discussion too. My captain once did the same with his Mod. 36 S&W, much to the chagrin of the onlooking deputies.............
Anyway..................
The best .22mag round for dispatching DEER, is the Winchester 40gr jhp.(or similar rounds from other manufacturers). The FMJ and TMJ's WILL completly penetrate and can cause an additional hazard to bystanders with headshots, and most usually will completely penetrate with a broadside chest shot. Ask me how I know....BTDT. Also, the jhp's will expand giving better shock and trauma rendering the animal much more quickly incapacitated. (shatters the cranium on headshots). (See episode involving the 9mm FMJ above).
For "poaching", I saw much better effect from the .22Hornet in rural settings. But it's not as quiet as you may think. In more settled areas, even the .22mag was unmistakeable. The .22rf was much more desirable from the poachers point of view, but, it's hard to "escape" when you are being watched and videotaped with nightvision gear which is now ubiquitous with even the most cash strapped agencies. We even had remote sensors to include seismic and infrared motion sensors and remote computer downlinks on our covert units........ but I again digress............
I utilized the .22mag and equivalent loads (cast bullets in a .22Hornet) on a number of occasions. One that particularly stands out was a smallish 8pt buck that had been chased (witnessed) by a larger deer and jumped into an empty concrete holding tank at the local municipality water treatment plant. The staff wanted the deer (alive but with two broken legs) "euthanized" but didn't want a round busting the concrete and causing $,$$$,$$$ damage and further repair cost to a unit already down for maintainance. The "hornet" with the cast bullet load did nicely. I had the deer out and was leaving and the plant manager wanted to know why I was leaving so soon, already................
On another occasion, a yearling buck (small spikes) had gotten over(under?) a "deer-proof" fence into a backyard-community/swimming pool compound. Efforts to flush the deer out had been unsuccessful and the residents were leaving for the weekend and didn't want the deer getting onto a pool that had been covered for the winter and were afraid the deer would damage the cover. The "lady" practically swooned when I removed the bull barreled and target -scoped 10/22 from the pickup. 5minutes later as I was driving off with the dispatched deer, the husband wanted to know what I was going to do about the deer. I said I was taking it to the County jail where they would make hamburger of it. His puzzled look was sufficient for me to point to the bed of the truck. He looked in and asked "how did you do it?" I stated, "head shot". He said..... I didn't hear you shoot! I stated...... its just a .22!" He replied "WOW", I didn't know a .22 would do that! (CCI minimag hp to the left ear at 50' -not much noise, >>>>>> but a lot of blood !) (What, no earth shattering Kaboom............... there was supposed to be an earth shattering kaboom..............) (.22lr)
shot placement, shot placement, shot placement!!!!!!!!!!!!!!!!!!!!
but: do use "enough" gun.
However; "Enough" can depend on the circumstances.
And, know your equipment and it's limitations.
My choice of a survival rifle would be a takedown .22mag with an assortment of ammo.
Cost, weight, power, compact size, accuracy.
Ammo is only slightly more bulky and heavy than .22rf but ~3-4x more powerful. Only ~1/2 less powerful than much more expensive .22Hornet.
And, in a pinch (survival situation- aircraft forcedowns, for instance) CAN take larger than "small" game if neccessary.
Hell, this ain't bad, though. I've seen threads dug up from 2003. 
