ASME Section IX and AWS D1.1 have different mechanical testing requirements. In addition to the mechanical testing differences, the bend test jig dimensions may not be the same. Further, the acceptability requirements are not identical. However, you could weld two identical coupons and test one to ASME IX, the other to AWS D1.1...or use a big enough specimen and test and document accordingly for each code.
Having said that, AWS D1.1 Clause 4.2.1.2 allows the Engineer to accept for use a WPS qualified to another standard...in this case ASME IX. I would not recommend this as this becomes 'sloppy' should a critical weld fail and the regulator place the onus on you/your organization to explain why this was performed.