Currently most OBIEE 10g users plan to migrate to 11g. They install the newest 11g version and play around. But be aware that you can not migrate from 10g (10.1.3.4) direct to 184.108.40.206.1 or 220.127.116.11.2. You have to run the upgrade assistant on 18.104.22.168.0 and then patch to 22.214.171.124.2. Oracle says in Oracle Support Note 1488803.1 “A direct upgrade from 10g to 126.96.36.199.2 BP1 is not supported”. Hopefully a direct migration to 188.8.131.52.3 would be possible again.
Read more about supported upggrade paths: click