I own and use both a Henry carbine .22lr and a Savage bolt action .22mag. As stated above the ammunition is not interchangeable. However in the .22lr you should also be able to use .22 long and .22 short, as long as It's not an autoloader. I use both for pest control, and find the Henry loaded with .22 short ammunition or shotloads to be effective on small varmints such as rats, or those pesky red squirrels that keep wanting to take up residence in the attic. I think it's also worth mentioning that .22 short/shotloads are considerably quieter to shoot than .22lr.
The Savage .22mag is scoped and used for larger pests at longer distance. I can attest that it will put down a rabid fox at 50yds without difficulty, but with considerably more noise/muzzle blast than the .22lr as well as the increased ammunition cost.
Not knowing what your needs are I would suggest the .22lr, I feel overall it is the more versatile and economical of the two.
That being said, the .22mag is one of my favorite cartridges, and if you feel a legitimate need for the increase in power I wouldn't hesitate to go that route instead.