Originally posted by bm75 DA60-250 and Sigma 150-500 are lenses that suit different purposes...In my opinion a lens like the sigma calls, ie for a sturdy tripod + head
I use my 50-500 handheld, and I'm not a bodybuilder. IMO it's a manageable weight for wildlife and airshows. The Sigma 150-500 weighs a fraction less than my 50-500.
To the OP, consider the 150-500 if you are most interested in taking photos of things very far away, or small things at medium distance. The Pentax 60-250 is lighter and wider aperture which can help in dim light or if you want thinner depth, but you sacrifice magnification in return.
In other words, for birding in good light I would favor the Sigma 150-500.
For indoor or night sports, I would favor the Pentax 60-250, assuming you can get reasonably close to the playing field. The 60-250 is also more of a general purpose lens if you want to do portraits.
Birding in dim light, or dim sports when you are sitting way back: Neither lens is ideal. Those are very challenging shooting conditions. That's why some people will pay $5K+ USD for a 500mm f/4. I'm not saying that to discourage you, just giving reasonable expectations. You
might be able to get good results with the Sigma or the Pentax or you might not.