I have seen a lot of people (especially professionals) buy Tamron or Sigma alternatives initially, use them for a while and then eventually transition to an OEM lens instead for better overall performance and quality....
Actually, Tokina makes a 70-200, too.... but it's an f/4 and only available in Nikon mount. It's also Tokina's first and only lens using ultrasonic focus drive and providing image stabilization.
While they're more expensive initially, if at all possible - as a few others have suggested - I also recommend just going straight to buying Nikkor for Nikon or Canon for Canon, assuming one of those are the camera(s) you use. (I omit Sony only because I don't know how the quality of their 70-200s OSS f/2.8 and f/4 compare to available third party lenses.... I do know they're pricey, similar to the most expensive Nikkors below.)
The Nikkor AF-S 70-200mm f/2.8E "FL" VR is excellent, but it's also
VERY expensive... around $2800 US. The previous Nikkor AF-S 70-200mm f/2.8G VR was a fine lens too, might be found for a lot less (but is hard to find new, now). The Nikkor AF-S 70-200mm f/4G VR is more compact and lighter, also an excellent lens, for $1400 (tripod ring sold separately for $165).
Just yesterday Canon announced new 70-200mm f/2.8L IS "III" USM and 70-200mm f/4L IS "II" USM lenses. The f/2.8 lens will be selling for $2100 (no price increase over the previous "II" version) and the f/4 for $1300 (a $100 increase over the previous model). The new versions are not in stores or reviewed yet, but on paper they appear to be relatively minor upgrades. The f/2.8 mostly sees some improved coatings on elements and is getting a new IS system (now with "mode 3", same as other recent top-of-the-line Canon IS lenses). The f/4 lens is seeing similar, plus an 9-blade aperture (up from 8-blade) for slight improvement of background blur. The f/2.8's IS is rated for 3.5 stops of assistance (no change?), while the f/4 lens' IS is rated for up to 5 stops (an increase from 4 stops). The new f/4 II also is slightly increasing in diameter, has gained just a little weight (+ 20 grams = 5 standard paper clips) and will use a larger filter (72mm versus 67mm) and a new lens hood (included) with a more secure "latch" mechanism same as Canon has been fitting to other new lenses the last few years. The f/4 II is also getting a new optional tripod ring (not included, sold separately), which also is somewhat more expensive ($210 versus $145).
These new Canon models will no doubt be excellent. But they also are causing discount pricing on the models they're replacing, which are still superb, pro-quality lenses that buyers might want to consider if they're a Canon user. I've been using both Canon f/2.8 IS and f/4 IS versions for years. Great lenses! Very fast focusing, durable, tough, well sealed, with excellent image quality and helpful stabilization.
All the Canon lenses here use fluorite elements, same as the Nikkor "FL" (first of it's kind to do so). AFAIK, none of the Sony or third party lenses use fluorite, which is an ideal material to reduce chromatic aberrations in telephoto lenses, as well as save some weight. But it is expensive because it's a difficult material to shape into lens elements and rare to find in sizes large enough for that purpose. Sigma uses "FLD" elements in many of their lenses, which they describe as "fluorite-like", but aren't actually fluorite.
Decades ago Canon pioneered growing their own fluorite crystals under controlled conditions, as well as developing some manufacturing processes working with them. They've used fluorite in many of their telephotos since the 1980s... In fact, their use of fluorite is purportedly why Canon started painting many of their lenses white (other manufacturers have done the same.... to reduce heat gain and metal expansion, which might in some extreme situations damage fluorite). "Big white Canon lenses" have become almost a trademark now, and all but a few of them use fluorite. But some Canon using fluorite sell for as little as $600 (70-200mm f/4L non-IS version). Over the last year or so Nikon revised all their primes 400mm and up, as well as their 70-200mm f/2.8 to use fluorite. At $2800, the latter is the least expensive of their "FL" lenses. Nikkor FL lenses are still being painted black, BTW.
You can do head-to-head test image comparisons of many of these lenses at the-digital-picture.com I'd strongly recommend you do so, to help you make your decision. Also carefully read reviews regarding AF performance, build quality and sealing for weather/dust resistance, compare the effectiveness of image stabilization, size and weight, and more. For example here's image quality comparison of the Sigma OS HSM versus Tamron VC USD G2:
https://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx?Lens=806&Camera=453&FLI=0&API=0&LensComp=1116&Sample=0&CameraComp=453&FLIComp=0&APIComp=0 (Doesn't matter what camera the lenses are tested upon, so long as it's the same or as similar as possible.)
To my eye, the Siggy and Tammy G2 look quite similar in the center, wide open at all focal lengths... but the Tammy appears sharper in the corners (which might not matter is using on a crop sensor camera). Switching to compare the Canon "II" with the Tammy G2 Their images appear quite similar at 70mm, but the Canon looks sharper with better contrast across the frame at 200mm.
You'll also find Bryan's extensive, detailed reviews for most lenses there, as well as other head-to-head comparisons (distortion, vignetting, lens specifications, etc.)
While the-digital-picture.com's primary focus is Canon gear, there are lots of tests and reviews of other brand gear there too.
Actually all manufacturers have put a lot into developing 70-200s, it's such a popular and important type of zoom. As a result, they're probably a lot more similar than different in most respects. Choosing among them may come down to some small difference in features that cause you to opt for one over another. For example, I really like that Tamron G2 series lenses with tripod rings now have an Arca-compatible dovetail built in.... that's both more secure than an added lens plate
and it saves the additional expense buying a lens plate or a custom replacement foot or ring ($30 to $120, approx.) IMO, it's a simple but really thoughtful feature for Tamron to include. I hope other manufacturers start picking up on the idea and doing the same. It's a minor think, but doesn't in any way effect use of the lens without Arca-type quick release system... so little reason not to do it (take notice Canon, Nikon, Sigma, Sony, etc.!)