Haskell - WITHOUT loading source - 478 644 characters
This assumes getContents ALWAYS ends with a newline and so drops the final character without checking because I don't feel like escaping it
A
main=interact$($'1').replicate.(1-).fromEnum.(/=map r(d++shows d[toEnum 10]))where r n|n=='-'='*'|n=='*'='-'|True=n;d="main=interact$($'1').replicate.(1-).fromEnum.(/=map r(d++shows d[toEnum 10]))where r n|n=='-'='*'|n=='*'='-'|True=n;d="
B
main=interact$($'1').replicate.(1*).fromEnum.(/=map r(d++shows d[toEnum 10]))where r n|n=='*'='-'|n=='-'='*'|True=n;d="main=interact$($'1').replicate.(1*).fromEnum.(/=map r(d++shows d[toEnum 10]))where r n|n=='*'='-'|n=='-'='*'|True=n;d="
It works like a standard quine, but swapping - for * to get the other program (avoiding those characters elsewhere).
The following test prints as expected (replacing main=interact$ with a= and b=)
main=do
putStrLn "START"
putStrLn$a "FOO"
putStrLn$a "main=interact$($'1').replicate.(1*).fromEnum.(/=map r(d++shows d[toEnum 10]))where r n|n=='*'='-'|n=='-'='*'|True=n;d=\"main=interact$($'1').replicate.(1*).fromEnum.(/=map r(d++shows d[toEnum 10]))where r n|n=='*'='-'|n=='-'='*'|True=n;d=\"\n"
putStrLn$b "FOO"
putStrLn$b "main=interact$($'1').replicate.(1-).fromEnum.(/=map r(d++shows d[toEnum 10]))where r n|n=='-'='*'|n=='*'='-'|True=n;d=\"main=interact$($'1').replicate.(1-).fromEnum.(/=map r(d++shows d[toEnum 10]))where r n|n=='-'='*'|n=='*'='-'|True=n;d=\"\n"
putStrLn "END"
-
START
1
1
END