The 270, properly loaded is fine for elk. The guns are both great choices, but are on opposite ends of the spectrum. Decide what features are more important to you.
The Vanguard is among the heaviest of all rifles. You will be over 9 lbs once you get a scope, mounts, sling and ammo on it. Maybe close to 10 lbs depending on your optics. That is a lot of weight for a mild recoiling 270.
The Tikka is the lightest rifle you will find under $1,000. If you chose your scope carefully it will come in under 7 lbs and be much better to carry in the elk mountains at 9,000 ft or more.
The Vanguard is more traditional looking with more aftermarket support. The Tikka has very modern styling that turns many people off. The Vanguard uses a 5+1 mag with traditional floorplate. The Tikka uses a 3+1 detachable magazine that is overpriced and hard to find spares.
Both have a reputation for excellent accuracy, but with the examples I've owned and shot I have to give the edge to the Tikka.
You can find the older Vanguards on closeout prices for around $350, the newer S-2 versions are around $470. The Vanguard is certainly the most rifle for the money right now. A Tikka is a bit more expensive, but does come with scope mounts.
If I were buying it for me the substantial weight savings, and slightly better accuracy in my experience would lead me to the Tikka. Especially in a 270 or other mild recoiling rifle. In a harder kicking magnum the choice would be a little harder, since some weight would be a good thing.