The first thing that you have to understand is that in today’s cartridge landscape, there is a LOT of overlap. While that can make it difficult to decide exactly which way to go, the good news is there is also little chance of making the wrong choice. Simply because there are so many RIGHT choices.
First, since you’ve narrowed the brand of rifle already, we need only address chamberings that are in Tikka’s current stable. Tikka doesn’t make a 7 Short, only a conventional 7 MM Rem Mag, so that narrows things down considerably.
There is no doubt, the 270 WSM is a good cartridge and fully up to the task of elk while not being so overblown that it’s too much for deer. The added benefit of the 270 Short is just that–it’s a short action. How much that matters to you is down to personal preference.
The knock against the 270 short is the cost of ammo (if buying off the shelf) and the limited overall offerings. Also, it does not represent a big departure from the .30-06 you already own. And just ask any outfitter, they will verify that a LOT of elk have been taken with vernerable ought six.
With the conventional 7 MM Rem Mag, you’re stepping up into a long action and, again, there is lots of overlap with the 06.
But the 7 MM has been and will continue to be around for lots of good reasons. It shoots flat and there is a huge selection of top-performing bullets. The 7 MM may also have a modest advantage over the 270 WSM in terms of the availability of factory ammo.
If you’re going to really depart from where you stand now, the “step up” option is clear: The 300s. The classic Win Mag or the WSM.
Obviously, you’ve put your finger on the key disadvantage. Recoil increases. The problem is you can’t fight the law. In this case, the law of physics. More = more.
But really, have you shot a .300 Win Mag or equivilent 300? I’m no sadist in terms of recoil, but it isn’t THAT bad. Get a decent pad fitted and shoot off of a lead sled when bench testing and it’s liveable.
The advantage is that the .300 class is a clear performance upgrade over both what you own and the 270 Short. You are going to shoot flatter and hit with more authority with a .300, especially on bigger game where it will be desireable to have more bullet options in higher weight classes.
Obviously, it is no accident that the .300s are the King of the Elk Rifles. Big, hard-hitting, and with lots of knockdown power even taking into account the poor bullet performance of yesteryear compared to today’s bullets.
Again, the good news is that there really isn’t a wrong choice here. I would say much depends on how much you want to bias the rifle toward elk hunting as opposed to getting a versatile, all-around performer that can be used for elk.
Grouse