UT and RT effectiveness is similar, but each have their pros and cons.
Whether or not you can present an approvable case for revision to the customer depends on the type/orientation of defects you're specifically looking for.

For example:
If porosity is a concern, RT is better.
If hairline cracks are are concern, UT is better, with limitations on crack orientation.
Some highly critical inspections require 2 or 3 differing NDT methods for ultimate assurance.

There is a boat load of info about this and more in the archives of this forum. I recommend a search.
Here's a good place to start:

https://app.aws.org/forum/topic_show.pl?tid=18583

In addition to what Tim mentioned, you also need to consider the alignment of the joining members, geometry of the weld and any thing which may restrict the examination (like a nearby gusset or drilled hole), the surface roughness, as well as access to both sides of the joint.  It is also worth mentioning that RT provides a permanent record, so it allows for others to review the radiographs.  Depending on the type of equipment, UT may not provide a record. You should also consider the skill level of the UT technician.

One thing I always mention to my customers that do not routinely weld joints that will be inspected with UT is to visually inspect after each pass paying special attention to the edges of each pass, and to use run-off tabs to avoid starts and stops in the weld itself.  On piping connections, I advise grinding each start and stop to confirm there is no lack of fusion or inclusions.

eakkapong,
They are both volumetric tests. They will be called out in the contract documents for your customer ( as you stated).
RT in my opinion, gives the best overall clarity, but can cost a lot of money when they arrive and have to shut down half the job site. and UT can be done on some fillet joints and other that RT can't. Check out 6.11