Wasn't able to confirm your issue using a text field. Something is altering the field or something of the sort causing it to think the values are different. Using the below example I was able to test the conditional.
Type: Redirect
Triggers: onAfterUserUpdate
Access: Everybody
Conditional: [cb_text] Not Equal To [var3_cb_text]
URL: index.php
Message: New: [cb_text] - Old: [var3_cb_text]
Note the action has no affect on how a conditional behaves. The conditionals are done before the action even does anything.
You can try using the POST values as well if needed. For example [post_FIELDNAME]. There is also cleanup functions available. For example could do the below to remove whitespace surrounding the string.
trim([cb_ortrechnung]) Not Equal To trim([var3_cb_ortrechnung])