Heya,
Get the one that has the best deal for you, they're equals image quality wise in reality. The OS is probably better on the Sigma for all modes. The Tamron would hopefully have the new firmware to make it's VC appropriate, if it's an older model (first release cycle) it would need that update to get panning and stuff right on the VC. Again, image quality wise, they're a wash. Both can be used with a 1.4x TC and a camera capable of F8 focus. It stays relatively sharp, but it's a noticeable hit. The AF accuracy is going to be poor though, so don't expect much in terms of tracking a moving subject. Ideally, don't use a TC. If you want supreme reach with IQ/sharpness/speed, save up for an appropriate lens for that. If you get one of these, be ok with 600mm at F6.3.
I have an initial release Tamron, no firmware update. It's tack sharp. Focuses fast. I've felt no need to replace it or update it. That said, it was the only 600mm available for $1k back then. Now that there are other options, I would have to be more critical, and since they cost the same basically, I'd probably buy the Sigma if for nothing more than the better OS and the USB dock option (not that I need it, but it's nice to have that option if you do need it).
Note, Tamron is releasing a USB dock as well, but as of right now, it only supports the latest VC primes. So it's not certain if it will support the 150-600 VC, but hopefully with a firmware update it will, otherwise, Tamron would be shooting themselves in the foot.
I will say this, the Tamron warranty is awesome and they service here in the USA and they are responsive.
Overall, learning what I have from these lenses, it's done nothing but prep my wallet for a 300 F2.8 or 400 F2.8. Even with all the reach, you end up wanting something else...
Here's some from my first gen non-updated Tamron:

IMAGE LINK: https://flic.kr/p/napzba
IMG_0923
by
Martin Wise
, on Flickr
IMAGE LINK: https://flic.kr/p/npdm8o
IMG_3484
by
Martin Wise
, on Flickr
IMAGE LINK: https://flic.kr/p/q1dFyx
IMG_1953
by
Martin Wise
, on Flickr
IMAGE LINK: https://flic.kr/p/rinyRE
LE1M1624
by
Martin Wise
, on Flickr
IMAGE LINK: https://flic.kr/p/rqFnEt
IMG_3849
by
Martin Wise
, on Flickr
IMAGE LINK: https://flic.kr/p/rnc5Q1
IMG_3682_mark
by
Martin Wise
, on Flickr
Here we are with a 2.0x TC (Kenko PRO 300 Series DGX) for 1200mm:
IMAGE LINK: https://flic.kr/p/peego2
600mm + 2.0x TC (1200mm)
by
Martin Wise
, on Flickr
And here's no TC, bare lens:
IMAGE LINK: https://flic.kr/p/DRkup7
IMG_0400B
by
Martin Wise
, on Flickr
Very best,