I want to use full-sized, as in:
Click here to download a full-sized version of this image.
- full size
- full sized
which would you employ and why?
From Collins Cobuild English Dictionary:
full-size or full-sized A full-size or full-sized model or picture is the same size as the thing or person that it represents.
So, I would choose one of those options and trust the dictionary.
I really couldn't decide between full-sized and full-size in your example: both would be perfectly fine and common. Note that you need the hyphen in either case, because it is a compound adjective (an adjective composed of more than one word) and it comes before the noun it belongs to. If you put it after, you don't need the hyphen: this picture is not full size. (Note that it is often more stylistically pleasing to use a different construction in that case.)
Either option is correct and usable. Both they have slightly different emphases. "Full-size" indicates that it is of the right size, while "full-sized" may additionally imply that it was deliberately made to that size. It's a very slight difference.
@Cerberus is correct that no hyphen is used when you put it afterwards.
The Google Ngram in the original question is flawed. You must put parens around a term containing a hyphen. Try the search again using these terms: (full-size),(full-sized),full size,full sized
You will get a completely different result with 'full-sized' being by far the most common followed by 'full-size'.
Try this corrected Google Ngram
I would use full-size. Compound adjectives preceding a noun should be hyphenated, unless the compound modifier includes something like more, less, least, etc.
Another pretty reliable test for hyphen necessity is to check whether the second element in your compound modifier can stand on its own.
In the case of 'full-size file', for instance, could we just have a 'size file'? In the case of 'full-sized' file, it seems to me that we could have a 'sized file,' but as shipr pointed out, this gives the impression that the file had the action of sizing applied to it.
Logic (as adequately noted above) is on the side of full-size; usage is on the side of full-sized.
(Interestingly, the OED does not even list size as an adjective.)
The same logic speaks in favor of age instead of aged (They have one child, age three.) and old fashion instead of old fashioned.