The scanner the archives use will produce the best copy of the original it can, depending on the state of the register. The scanner they use cannot improve the quality of the original document.
The output can then be sent to you on a cd, dvd or email as a pdf or jpg.
Or you can elect to have a paper copy sent in the post. But then you would have to make arrangements to scan the paper copy at home and save the document onto your computer. If you don't do that, the paper copy may become damaged over time.
I would opt for the digital copy if it was offered to me.
Each time you scan a document and get further away from the original, you loose a bit of the quality.
There could also be a difference in the price which may swing your preference.