1.4 extender or crop?

Full frame + extender.
In fact depending on the two cameras, you could be better off with the full frame even without extender and cropping in PS. I took some nature shots with a very cropped bridge camera at 600mm and at the same time captured the same images with a full frame DSLR at 200mm. Once cropped the FF shots were much better Image Quality but this was not a big surprise as the DSLR sensor is 32 times bigger than my bridge camera.
In fact depending on the two cameras, you could be better off with the full frame even without extender and cropping in PS. I took some nature shots with a very cropped bridge camera at 600mm and at the same time captured the same images with a full frame DSLR at 200mm. Once cropped the FF shots were much better Image Quality but this was not a big surprise as the DSLR sensor is 32 times bigger than my bridge camera.

An extender on 24x36 with a decent lens generally produces a little more image resolution than cropping in post processing. This can be offset by a slightly dimmer viewfinder and slightly slower AF.
With a crop sensor body, technology for technology, there is usually little or no reduction in dynamic range, resolution (MP for MP) and no loss in noise performance to at least 400 ISO and maybe 800. Benefits are generally a brighter viewfinder and fast AF compare to using a 1.4x.
I know this is a Canon question but with Nikon there is little resolution difference between D850 45 MP cropped to 20 MP D500, though the D500 AF points cover a bigger percentage of the screen.
A minor detail is a 1.4 x crop is usually slightly less than switching to a 1.5 or 1.6 x "crop sensor" body.
With a crop sensor body, technology for technology, there is usually little or no reduction in dynamic range, resolution (MP for MP) and no loss in noise performance to at least 400 ISO and maybe 800. Benefits are generally a brighter viewfinder and fast AF compare to using a 1.4x.
I know this is a Canon question but with Nikon there is little resolution difference between D850 45 MP cropped to 20 MP D500, though the D500 AF points cover a bigger percentage of the screen.
A minor detail is a 1.4 x crop is usually slightly less than switching to a 1.5 or 1.6 x "crop sensor" body.

Quote:Which would produce the best image, one that digitally zoomed,(crop camera) or one thats optically zoomed. (FF + extender)
Not quite sure where that digitally zoomed bit comes from....
What counts is which one will place more pixels on your subject and that with a few exceptions you will always be after more focal length, you may find that even with a 1.6/1.5 crop body you will be adding the 1.4 extender.... For what it is worth I tend towards a 1.3 crop body.
Edit... Len beat me with a slightly similar reply.