Well, in for a penny.
I'd say an 1813 barrel would be worth less than a 2013 in similar condition. Firstly any 2013 will be younger than any 1813; the 2013 was introduced in about 1991, whereas the 1813 was replaced in 1987, and production started in 1980. In this case the seller may well be the original owner, and knows the full history, but when a rifle is sold 3rd or 4th hand and there is no provenance, it's not unreasonable to assume an older barrel has a higher "mileage". Even if the rifle is shooting well now, higher mileage means it may loose accuracy sooner. Secondly the 2013 has always been more expensive than Match 54 rifles, which should carry over the second hand prices.
The rifle in the photos does look very clean and tidy.