Sony 70-300G vs. Tamron 70-300 USD

I have an A77 with the 16-50 "kit" lens.  I would like to now expand by getting a new zoom with much longer reach.

I primarily will use the lens with my 5 year olds and their fast moving activities (soccer, playground, parks, etc.) and also when we go on vacation specifically for things like mini-safaris and the like.

I want a lens which will greatly extend the reach of my current lens with great IQ, fast and very quiet focus (for video) and I want to be able to use the focus peaking which I really like.

As far as I can tell from the research I've done these two lenses seem to be the candidates but with a huge price difference.  The Tamron for $350 after rebate and the Sony for ~$800 in like new condition (with warranty).

So for anyone that has used both of these lenses, what would you suggest?  I can afford the Sony if it is that much better, but that also means cutting back on other lenses I can buy in the near term.