CJam, 21 bytes
qe#ere$_"}{][><)("%Wq
[Test it here.][1]
Normal reversion:
qW%"()<>[]{}"_$ere#eq
[Test it here.][2]
Visual reversion:
qW%")(><][}{"_$ere#eq
[Test it here.][3]
Explanation
First, the normal code:
qe#ere$_"}{][><)("%Wq
This is simple: q reads all input, e# comments out the remainder of the program, and the input is printed implicitly at the end.
Now the normal reversion:
q e# Read all input.
W% e# Reverse it.
"()<>[]{}" e# Push this string.
_$ e# Duplicate and sort it. However, the string is already sorted
e# so we just get two copies of it.
er e# Transliteration (i.e. character-wise substitution). But since the
e# source and target string are identical, the reversed input
e# is left unchanged.
e#eq Just a comment...
And finally, the visual reversion:
q e# Read all input.
W% e# Reverse it.
")(><][}{" e# Push this string.
_$ e# Duplicate and sort it. This gives us "()<>[]{}", i.e. the
e# same string with each bracket pair swapped.
er e# Transliteration (i.e. character-wise substitution). This
e# time, this toggles all the brackets in the reversed input
e# completing the visual reversion.
e#eq Just a comment...
[1]: http://cjam.aditsu.net/#code=qe%23ere%24_%22%7D%7B%5D%5B%3E%3C)(%22%25Wq&input=qe%23ere%24_%22%7D%7B%5D%5B%3E%3C)(%22%25Wq [2]: http://cjam.aditsu.net/#code=qW%25%22()%3C%3E%5B%5D%7B%7D%22_%24ere%23eq&input=qe%23ere%24_%22%7D%7B%5D%5B%3E%3C)(%22%25Wq [3]: http://cjam.aditsu.net/#code=qW%25%22)(%3E%3C%5D%5B%7D%7B%22_%24ere%23eq&input=qe%23ere%24_%22%7D%7B%5D%5B%3E%3C)(%22%25Wq