Either one is going to be a great hunting rifle, period.
It's mostly a matter of preference. Shoulder both rifles in a store, dry fire them to feel the triggers, notice the differences in the comb of the stock. The Weatherby has a raised cheek piece, the Savage doesn't. I prefer the shape of the stock on the Weatherby, but that's just me.
The factory trigger on the Weatherby, which is a 2-stage trigger, at is lightest will be between 2 and 2.5 pounds. The Savage accu-trigger can usually be adjusted down to 1.5 pounds.
Do you need a trigger as light as either of these to hunt with? Not really unless your shooting several hundred yards, but it sure is nice IMO to have a light trigger. Again, that's more of a preference thing.
The Weatherby has a 24" barrel, the Savage has a 22" barrel. The 24" will give a slight velocity advantage with the .270 cartridge, but not a whole bunch, maybe 100 fps or less. If maneuverability it tight places is an issue for you, the shorter barrel on the Savage might be more to your liking.
The Weatherby has a hinged floorplate, holding 5+1, the Savage has a detachable magazine, holding 4+1. If given the choice on a hunting rifle I will choose a hinged floorplate every time. If you are a fan of the detachable mag and want the Weatherby, they sell a DBM kit with 5 or 10 round mags and it's relatively inexpensive.
The Weatherby has a sub-MOA guarantee which is a plus, the Savage does not. But if you buy a Savage that doesn't shoot sub-MOA, there's more than likely something wrong with it and you should check a few simple things or send it to Savage and let them make it right for you. I have never seen a Savage rifle with a bore and crown in good condition, action screws tight, decent scope, etc. that wouldn't shoot MOA or better with the right ammo. I'd say they may have made a few, I've just never seen one. So don't let the whole guarantee thing sway you too much.
There's also a slight price difference in the two rifles. MSRP on the Vanguard is $1149, MSRP on the Savage is $922. Real world I'd say you should probably expect to pay about $850-900 for the Vanguard and $700-750 or so for the Savage. The difference is small enough IMO that you shouldn't really let it sway you one way or the other. Get the one you like best regardless of $100-200 dollars. You'll be happier in the end.
Don't let anyone talk you into or out of either of these rifles, because they are equally good at what they do. Find which one fits you best and go for it.