Specifically with regard to DRM I'd say they are just as ineffective, but more consumer hostile.
But this is all red herring since the TPP does not set any goals for measuring actual ENFORCEMENT, it only imposes new IP laws outside of the democratic process, with zero transparency, all while claiming to be a "free trade treaty".
Let's make it clear: Copyright laws have nothing to do with free trade. Let's suppose for a moment the US Copyright law is anywhere near "balanced" (and Canada is a caribbean pirate cove, as xxAA groups and the USTR love to claim). That still has nothing to do with Free Trade. If the Obama administration really wants to use TPP to fix all of the world's evils as they see them, why not push signatories to accept LGBT marriage for instance?
https://en.wikipedia.org/wiki/Supremacy_(European_Union_law)
As to whether it applies to all treaties or just the EU ones, ... good question. In practice courts haven't really followed it.
Also, just as a data point, I've been working in Brussels for close to 20 years now and seen the evolution. I work as a consultant, so it has been a mixed bag for me. However, for just about everyone else, workers, middle class, business owners, ... it has been a consistently worsening disaster.
Having regularly worked for the EU commission, let me tell you this : any idea you may have that this organization has anything but their own economic interests at heart can be cured by chatting with one of them for 5 minutes.
The TPP would not, in US law terms, be a treaty, but a regular federal statute.