IMO, there really is NO best rifle, its what you the shooter like best, what fits you the best and how it fits the intended role that you have for the rifle. There is a big different in price between both those rifles. The XCR tactical I THINK is more accurate then the Tikka and if you wish to customise the rifle then is the rifle that you should get. There is a serious lack of after market parts for the Tikkas and that means that customising them is very tricky.
How much shooting experience do you have?? If little to none. I would forget a .308 for the moment and buy a .22LR to learn the basics. I did and dont regret it for a second. I have a nice little CZ 452 Deluxe and its a really nice rifle and very accurate.
I agree with Quick on Tikkas verses Remingtons. Personal choice. Both are capable of exceptional accuracy. Personal preference plays a role. (I own a Remington XCR Tact in 308.)
Customizing a gun and obtaining parts are a factor when considering a plain jane base model but don't buy a Remington XCR to customize it. Buy a cheaper Remington for the action and then customize that. The novelty of the XCR is that it is a packaged deal. It's got a free floated, fluted, stainless blackened barrel in a Bell and Carlson stock. These are the two main customizations to a rifle (Barrel and Stock). It makes no sense to buy one to remove these parts. Simply put, I bought it because I didn't want to do much to it. I liked the way it looked (not the best reason to buy a rifle) and I didn't want to put much work into it. I am getting about 3/4 MOA accuracy out of the rifle with match grade ammunition, but a better shot probably would do better.
PS check out the reviews on the Tikka and Remingtons at Equipment then rifle evaluations above. Mel works hard to review equipment for the sight. XCR has not been reviewed but I would consider it similar to the reviewed rifles (but more money). Quick links below.
The Tikka is machined to closer tolerances than the Remington, this leads to better accuracy out of the box, supposedly. The MSRP on the Tikka Tactial is $1498 the MSRP on the Remington 700 XCR Long Range Tactical is $1332 or the XCR Tactical Compact is $1433 so there isn't a huge difference in price. I can sell the Tikka for $1,100 right now so that tightens the price up even more.
There is more aftermarket support for the 700 as everbody makes everything for them. Manners will make a stock for a Tikka though.
I have a Tikka T3 Tactical .308 and a 700 XCR in .338 Ultra (not tactical) and while this sounds like a cop-out, it really depends on what you're after. The two criteria that would separate the two in my mind would be "OUT OF THE BOX ACCURACY" and "UPGRADEABILITY"
If you want a factory rifle that's handy, well made, a joy to shoot and is <1 MOA accurate OUT OF THE BOX with factory loads, and 0.5 MOA with good handloads, than I'd definately take a hard look at the Tikka T3 Tactical - I really like mine! The trigger can be adjusted by a novice down to around 3-lbs,... the barrel is threaded so you can add the Sako muzzle brake which makes it recoil like a .243, the detachable 5-round magazine is a nice feature that comes stock, and the adjustable comb, though simple, works really well. All of these nice touches add up to one great rifle for the money which in turn, kicks the hell out of the XCR IMHO!
However,... while the Tikka is a great rifle for the money and will shoot as good as 98% of the shooters who buy it will want,... it is a 'factory' rifle and is not all that friendly to modifications. Most, if not all, of the gunsmiths I've encountered don't know diddly about the Tikka T3's and most don't want to know anything. So, if you're thinking of using this rifle as a 'fixer-upper' and heavily modifying it (barrel, stock, bedding, action trued,..etc.) you're better off getting a lower end Rem 700 and throwing some money at it and a good smith. My XCR is a lowend version and I put about as much into it as my Tikka by getting a new stock, bedded, muzzle brake, comb, 20moa base, etc. The one thing I like about my XCR is that I can do even more to it - new barrel, trued action,..etc. I won't be able to do this stuff easily with my Tikka,...but then again, I don't think I want to. Here's a target from this last weekend from a new load I was testing with my Tikka. While the whole 5-shot group was 0.306",... if you subtract the ONE flyer that killed the group, it comes in at 0.15",... not bad for a factory rifle in my book