OK guys. This is no definitive response - so consider it's worth.... but my short answer is the new Tamron 70-200 isn't any worse in low light compared to the newer HSM version of the Sigma 70-200. I cannot comment on any of the older versions as I've not seen or tried them to compare. Indeed the older Sigma 70-200s without the HSM motor are famed to be sharper and provide better overall IQ than the newer HSM version, despite Sigma's claims of improved quality in the HSM version.
I have toyed with both newer versions of the lenses very recently, the Tamron having had sticky aperture lever issues (but otherwise excellent quality in every aspect apart from pushing it to shoot wide open at minimum focus distance):
https://www.pentaxforums.com/forums/pentax-slr-lens-discussion/69207-request-...0-f-2-8-a.html, and the Sigma not impressing me both in its inability to take teleconverters currently available as well as its apparent sharpness issues:
https://www.pentaxforums.com/forums/pentax-slr-lens-discussion/72242-sigma-70...l-iq-test.html
But to specifically answer your question, I found both lenses locking focus reasonably quickly, and as quickly as each other, except for when focusing starts from the other end (i.e. trying to focus at something at infinity when the focus dial is starting from the shortest distance) - there, the Sigma HSM has the edge given its higher acceleration of the AF motor in the middle of the throw.
This minor difference to me doesn't sway my decision on which is best to get. I have never experienced the Tamron to hunt, although I have only ever used it in low-light concerts where spotlighting shines brightly enough to provide the lens with something to easily focus on. It has not failed me yet. So I personally cannot attest to your claims of AF difficulties with the lens - you may be looking at a lot of the Canon and Nikon reviews comparing the screwdrive Tamron versus the ultrasonic Nikon or Canon 70-200 lenses - between them there is a significant loss of AF speed, but between the Tamron and the Sigma on a Pentax dSLR, there is little difference to speak of.