ASME does not approve software; per ASME the design responsibility continues to lie with the designer (see the Foreword to Section VIII-1).
I suggest contacting each publisher and getting literature and a demonstration copy of the software. After you get familiar with each program ask the publisher for a free 30 day trial of the full software (demo versions may be limited in some way). Compare how fully each program is self-documenting....ie: in most cases they shouldn't just blindly spit out the end result, there should be some trail of calculation to follow. And compare how the programs list references such as Code paragraphs, tables, reference books, etc.
Be sure to check the user's list of customers to see how widely-used the software is and what the caliber of their customers are. Ask people you know at different vessel fabricators and engineering companies about their experiences with different programs.
Compare the technical support provided by each publisher. It's likely that you will regularly have questions about how the software works. How responsive is the support?
I believe that all three softwares are likely reliable; after all, they must meet the accuracy demanded by their customers and required for proper design or else they couldn’t stay in business.
In the end it is likely to be ones personal preference regarding the program interface, output reports, etc.