If you didn't trust the closed source disassembler you use, for whatever reason, you would verify the assembly output, not the actual software. In practice this is often done unintentionally anyway: it's common to run a debugger (ex: gdb, windbg) alongside an annotating disassembler (like IDA). objdump (from GNU binutils) also supports many non-Unix executable formats, including PE (Windows) and Mach-O (OSX/iOS).
For fun I just compared objdump's entry point function assembly of a downloaded Pokemon Go IPA to the Hopper representation, and, no surprise, they are identical.
For fun I just compared objdump's entry point function assembly of a downloaded Pokemon Go IPA to the Hopper representation, and, no surprise, they are identical.