Filtering two files with uncommon column

[Madhur]

I would like to know the best way of generating filter of two files
based upon the following condition

I have two files. Contents of the first file is

File 1
abc def hij
asd sss lmn
hig pqr mno


File 2

jih def asd
poi iuu wer
wer pqr jjj

I would like have the output as
Output

File1
asd sss lmn
File2
poi iuu wer

Basically I want to compare the two files based on second column. If
the second
column matches on both the files do not print anything, else if there
is no matc
h in for the second column for first file in second file then print it
under Fil
e1 header, else if there is no match for the second column for second
file in fi
rst file print it under File2 header.

Thankyou
Madhur