Your current computer dates to around 2013, and the CPU in it was a pretty good performer up until quite recently.
The Xeon equipped computer you've found dates to around 2010, while it looks like a good deal, it's really not worth anything, it's a used refurb that is at, or beyond end of life and your current computer is 30-40% faster. It is best avoided.
Moving to Windows 10 might give you some small improvements, but the only good reason to move would be for security as Windows 7 is no longer supported.
But, there are somethings you could do.
If you don't already have an SSD then installing one for the operating system and programs would make a noticeable difference.
A 250GB SSD is very affordable, and a a 500GB or a second 250GB would allow you to put images on it to work from for another increase in performance.
You could look for a second hand higher spec CPU, an i7 4770K would be a direct replacement and combined with an SSD it would make a 20-30% increase in performance.
With your motherboard and an aftermarket cooler you should be able to lock the boost frequency of all cores (also known as frequency sync) to increase the performance even more.
That would cost about half as much as the Xeon you've found, and be considerably faster (easily twice as fast). You could then sell your current CPU to make the upgrade even cheaper.
The Quadro card you have is rather outdated, but your not doing anything that is GPU intensive, so moving to a high spec card won't help performance wise.
Beyond that, the next step for a real massive boost in performance would be a new current generation CPU which would also mean a new motherboard and DDR4 Ram.
You should be able to keep the case, power supply, hard drives GPU etc.
But you don't need a whole new computer, you can upgrade the current one easily enough and get better performance than the HP Z600 for less money. Or for more money get a considerably faster CPU, motherboard and RAM for a computer that is 2-3x faster.
