Thanks an really interesting test. As you've managed to show that there really isn't much difference comparing 2000px wide Jpgs that show some compression.
If thats all your images are ever going to be finalised as and viewed on screen at 50% then the 650 will be just great.
However... The view selected isn't the best for a proper test I think. Try subjects with smooth tones and darker gradients plus interesting detail and then you'll see the noise & sharpness when especially viewing or working on them in RAW or at least tiffs in photoshop viewed 200%.
Try some nicely lit portraits or some well composed architecture and there will be a big difference.
But its horses for courses really, if you're just going be shooting what we might call messy scenes like this and kids running around and holiday pics then it might not well be distinguishable to FF instantly.
More than anything it will them more come down to your technique to get the best out of FF, framing, catching beautiful light and the moment together whilst selecting the 'optimum' shutter / aperture, iso and lens plus raw/post processing which can make a huge difference to noise & sharpness plus the grade to push a feel which can be more important than anything.
A good photographer can make APS-C look like FF or MFDB and a bad photographer can make FF look like P&S.
And the previous post that mentioned what about cropping.. well if you are constantly cropping your FF that much then
you shouldn't have FF or a DSLR in my eyes anyway