try rendering to sony mxf instead, then make an mp4 with handbrake, making sure to set the same parameters as the originals....

Try it and see.  I had the same color/contrast as you mention.  Changing the color rate to 8 bit (or 32 fixed) fixed the problem and made the render times faster.  This has to do with file types and post processing for correction from what I understand.
 
 

Cool, I'll give it a go, thanks!

If you plan to do any color correction, changing to 8 bit is a bad bad idea.

No the problem is the colors (and mainly contrast I think) are different from the original without me changing anything. I would love any suggestions for how to keep them the same. I've already matched project setting to source material but it's still different.

I suspect the issue might just be that you're viewing a .mov on the timeline and hoping to get the same color balance when you then again re render to .mov.
I've never had good results with .mov in any situation and I'd expect inconsistencies if I had to load one and re render it.

I always render to MainConcept AVC/ACC for the web with these settings and the results are great for me as far as I can see:




 
And when checking the properties of the media by right clicking on the media:


 
examples using these settings:
https://vimeo.com/98073619
 
https://vimeo.com/68400626

If I were experiencing the same issue, i.e. what I see on the timeline is not what I see when it's rendered,
I'd first render to a lossless file using Lagarith
Then insert that lossless render on an other video track in the Vegas project so I could compare to the original.
I'd then insert the color corrector or maybe also color balance onto the Lagarith video track and A/B with the original until I get it where I want it.
Then mute the original video track and render the final and compare.

If it was still and again different and not right then I'd suspect my render settings or chosen output format / codec are the issue.