First of all .. as you upgraded your PSU to a higher rating ... you also upgraded your components to a higher power rating. That completely negates the advantage of having a higher-powered psu. So the same problem could still apply.
So, pair up your new psu to your old lower-spec system. See if that changes anything.
If not, it's most likely a conflict in the OS itself. (ie windows). Either hardware in nature (eg IRQs) , or with the particular program/game that you are using, during which it restarts.
Here's what you should do.
First, determine where/when its happening. (eg Inside a game , inside Ms Word , while scanning for viruses with AV software, etc).
2) If its random (aka none of the above) , then check your hardware configuration such as IRQs (usually a problem not found on modern systems but can). Look for 2 identical IRQ numbers with 2 different hardware.
3) There maybe one or two settings not correct in the bios. So check that too. In this case write down the specifics and post it here so we can help you with it.
4) You could also try doing a fresh install on a new blank partition/ blank drive. Doing this "after" trying all of the above first is recommended.
This is also good advice.
i would also advise downloading Memtest
http://hcidesign.com/memtest/
and testing to see if you get any errors, memory errors can cause reboots too
...... and this
Is the memory all the same or mixed and match?
... by this I mean you could be running dual-channel memory configuration by using rams with different timings. I guess this could also be a factor. (Never tried it, but I think so)