I recently did migrate from 5.1 to 6.1
First make sure to create all the required resources like
JDBC,DataSource,Queue,Topics etc almost mirror the same configuration on 6.1.
Had some problems
1. If your application is using Messaging then you have to make litle change in your code.
Usually when you send message you open the connection then you create session and send the message and close the session but keep the connection open.Then for the next message you create another session from the same connection and repeat the step above.
But in case on 6.1 once the method call whcih sends the message is completed the WAS 6.1 automatically closes the connection and returns it to the connection pool but however it does not close the physical connection.
Please visit this link about this problem
http://www-01.ibm.com/support/docview.wss?rs=171&context=SSFKSJ&dc=DB520&uid=swg21267957&loc=en_US&cs=UTF-8&lang=en&rss=ct171websphere
2. If some of the jsp/struts code tag is not closed properly 5.1 somehow failed to detect them and renders the page but 6.1 will throw error.
It took about 5-6 hours for me to migrate.
Apart from these i did not face any problems
But ofcourse it depends on the application size and available resources.