@oldmanlongstaff: what brand of camera body are we talking?
I haven't used any of these, but let me warn you. Lenses that have a large degree of utility for focal length often suffer in the upper ranges. If this is something that is extremely annoying to you, or your looking to add something like this ontop of a teleconvertor then the higher focal ranges will suffer quite a bit. If you can find out the ideal ranges before they degrade significantly. It will probably help you choose better which lens to buy.
Some of the big things you will notice is Chromatic aberration, loss of focus and detail.
@oldmanlongstaff: I forgot how bad the info on Tamron's site is for info on their lens selection. I would be tempted to say go for the sigma. For one big reason, Optical stabilization. When you start getting to those focal lengths and your tracking stuff it makes all the difference in the world. 500 and 600mm without stabilization is rough. Even at 800mm with stabilization it can still be a difficult experience to track something at distance. as your field of view is extremely narrow, and tiny movements translate to huge movements.
While there is generally nothing wrong with tamron lenses, they are good deals in my experience. They are extremely loud, think RC car level of noise. This can be a deal breaker for a lot of people. Don't even think about shooting video with them on auto focus, all you will hear is the focus motor. In this situation spending close to 1000$ on stabilized loud lens seems like a deal breaker in my book.
The Tamron 150-600 f/5-6.3 Di VC USD is the real deal bought it last month from amazon http://amzn.to/1tzEFIS, It works just great for BIF , i love it so much
I'd say go with a prime. You might think that the zoom will offer lots of advantages. It does, but it pays to learn on a non-focusing lens that makes you do the work. A prime forces you to walk around. By doing so you will study your subject more before taking the shot and hopefully realize that the first view usually isn't the best one.
You will also be able to let more light into the camera with a prime lens. Even a $100 50mm f1.8 lets lots more light into the camera than the lenses you mentioned. You'll be able to have less noise due to high iso's this way or stop action more easily.
Primes past 150mm or so are all big dollar lenses no matter how you slice it. They are also more specialized, removing a large amount of the versatility that less experienced photographers will find frustrating.
I have no experience with large range telephoto lenses. but I have owned the Tamron 70-200mm F/2.8 VC for about a year now. It quickly be came my lens of choice. at about $800 less than the Canon its not as robust, its plastic over metal, but its also way lighter. I shoot large live corporate events for a living and the weight difference was a huge deciding factor. The focus is also quick and quiet too. So, yeah, I definitely champion Tamron.
Oh.... right... telephoto.... sorry about my previous post. I was not taking the telephoto aspect into account.
In that case, I second the 70-200mm f/2.8. Sometimes you can even get good deals on used Canon 70-200mm f2.8's that are a generation or two old. It's still good glass even though it's not the newest version.