Sigma 120-400mm vs 150-500mm

[Moellertime]

I am a relatively advanced photo hobbyist and I currently own a Canon Rebel XSI with the Tamron 18-250mm superzoom that I use as a multi-purpose lens as well as the Canon 50mm f/1.4 prime which I use for taking pictures of friends and family. Recently though I have started to get into wildlife photography and have found that my Tamron is not nearly long enough and that it is unacceptably soft past 200mm. Therefore I am looking for a long, relatively sharp telephoto lens to use for wildlife but would also like to be able to use it for sports such as football. My budget is $1,000 and I can absolutely not spend any more and would prefer to spend less (bigma and Canon's 100-400L are out) and I must have IS/OS/VC as I will often be shooting handheld. I think I have narrowed it down to one of these two lenses given my price range:

Sigma 120-400mm F4.5-5.6 DG APO OS HSM
or
Sigma 150-500mm F5-6.3 APO DG OS HSM

If anyone has another option under $1,000 please let me know

Now given the fact that will often use this lens for wildlife I'm sure you all would suggest the 150-500mm purely for the 500mm focal length which I admit would be nice however for my situation there are several benefits of the 120-400:

Lighter/Smaller: not sure I want to carry a four pound lens around that much and it might be hard to handhold

Faster: Even with OS I still think the faster aperture will come in handy while handholding

Wider: 150mm may be to long for some sports situations especially if I am close to the sidelines although I'm not sure if 120mm will be much better- I can always use my Tamron and just suck up the lower IQ

Cheaper: For most of you it might not matter but for me saving $100 is a good deal

Image sensor: remember I have a APS-C crop sensor so 400mm may be plenty of zoom

Anyone that has either of these lenses or knows a lot about them please give me your opinion of which one would be better for me or an alternative that would serve my purposes

Thank You!

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[Moellertime]

Sorry, I accidentally posted this in film and cant figure out how to remove it,I am reposting in digital, please comment and tell me how.