Now I am beginning to waffle but here goes. I was writing this before seeing the post above.
In my earlier reply I mentioned 'perfect' - I am aware that you haven't mentioned 'perfect' or seem to expect but it just seems that when looking at a new lens it is sometimes too easy to look at the problems without realising that everything is a compromise, for example - all zoom lenses appear to be a compromise of image quality over convenience and why else would 300/400/600/800 mm prime lenses exist if not for image quality over convenience - still a compromise exists
( ie fixed focal length/weight/cost - but the images are better than the equivalent zoom lens.
I bought the 70 - 300mm lens and found it's macro mode to be very good and even the 200 - 300 end not that bad particularly in the centre.
Another thing to think about is a shot of say a bird, a sheep, another animal or a sports player will usually have the main subject in the centre and the lack of sharpness at the edges can help to make the main subject to stand out in some ways slightly similar to a shot at a larger apeture will make the subjct stand out - lets face it the larger apeture shot from a better lens will be better and the outcome will have been reached for the right reasons rather than the lenses weaknesses - however, without pixel peeping/ bemoaning the laws of photography etc the effect is that the subject stands out - problems exist when you want more of the picture to be sharp.
I have some work arounds - these include, to zoom back to 200mm then use 300mm or another focal length of your choice - if the 300mm shot is not good enough try cropping the others to create a similar effect etc - not perfect but often surprisingly effective - or even cropping the 300mm shot - trial and error should only be of benefit by way of experience - and it the mean time to can save up for a more expensive lens if you feel the need. With a little practice you will know which you prefer and use that focal length more often.
The other way to look at this is you can spend say £160 on the apo sigma (£100ish for the Tamron or non apo sigma) or approx £500 for the Tamron 70-200 f2.8 or about £600 on the Sigma version and you have a faster apeture at f2.8 and better image quality. I cannot comment on the sony as I have not looked into that lens so I would be talking fertiliser and most probably misleading you.
With the f2.8's you have only 70-200, a lot more weight/size and have spent far more without even being able to take a shot at 300mm - does the 70 -300 look so bad now? - that will be your decision.
With regard to the increased shutter speed and greater control over depth of field offered by lenses such as the f2.8's - you can increase the iso to increase the shutter speed (another compromise) and for depth of field you can use software to mimick this effect, again a compromise - is this not part of the fun??
To finish off, I am sure that others will agree but some of the photo's people find the most pleasing are not always technically excellent or even close but still they are often more pleasing than others taken that are technically better
- equally some photo's have been ruined by poor photography skills/ poor equipment etc etc (even excellent equipment used badly)