I've owned and shot both (stainless savage, but regular blued X-bolt) side by side in .308.
I found the savage to be a little heavier (likely from the aluminum in the "accustock" that basically pre beds it for you). Despite the savage being a bit heavier the X-bolt with the newer style buttpad had less felt recoil. The savage buttpad is in no way bad, or insufficient, the browning's is just that much better. The barrel also seems a little thicker on the Savage.
If you shoot left handed i found the savage stock to be more ambidextrous, where the X-bolt was definitely biased to right hand, as i assumed the left hand model would be opposite.
The bolt handle on the X bolt seems quite slim, and the knob on the end is quite small, so with heavy gloves in late season it isn't the easiest to lift and cycle, but the 60 degree throw is nice, and with the smaller size lets it pass by your scope with lots of room. The savage bolt knob and handle are the typical beefy savage type, but it comes at a price. I found it comes a lot closer to your scope, and could require a bit higher ring, depending on the shape of it.
For triggers, the savage has the accutrigger, which i like, some don't, it's functional. The trigger on the X bolt is excellent different from what i am used to. It stays at the very back of the trigger guard, moves very very little before it breaks, and is quite light. I think it's probably the best trigger on any gun that i have. I did get the gun used, so i can't say if all of them will be good, or if this one has had any work done to it.
In terms of accuracy, i don't reload and have only tried blue box federal and nosler accubonds, and i am far from an expert markman, so take this section with a grain of salt. This was done on a bench with bipod on the front, nothing but me and my elbows at the back, and it's always kind of windy around here, so affects things and usually only shoot 3 shot groups. With the savage i average around a 4" group at 100m with the blue box federal, the nosler brought that to about a 3" group. With the X bolt i was getting around 3" with blue box and 2" with accubonds.
I actually think the savage is capable of better, and reading about it i feel like the Inflex Recoil pad on the browning, if it does what the website claims and reduces muzzle lift and all the other good things they claim, is what makes the difference more than anything else. I admit that i have some flinching, and i feel like i notice it pushing the butt up towards my face less helps this.
As for fit and finish, you get what you pay for. The browning is just that little bit nicer, smoother, etc.
If money isn't an issue, i would say go with the X-bolt and you won't regret it. If you plan to modify it, savage seems to have more aftermarket options than browning. And if budget is an issue, the savage will do everything you need it to, but the browning is just that little bit nicer at just about everything(except price tag).
If you find a good deal on one on sale, or good used price, neither will dissapoint.