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As you may be aware, developers used unregistered machine codes in their games, as discussed in this thread. My question isn't why they would do this, but instead if these instructions yielded a difforent result on the NES than it did on the Famicom. Keep in mind that these codes were tested to work on the Famicom, but Nintendo probably didn't care to make sure they had the same behavior on the NES, which was, in a way, a remake of the Famicom for American consumers.

To my knowledge, the NES and the Famicom had the exact same CPU (a Ricoh 2A03). So, it's unlikely there were any differences in behavior between the two with regards to undocumented opcodes. As the Ricoh had a 6502 core, you could also expect it has the same undocumented opcodes as the 6502 (not your question, though) - And this document seems to confirm this.

Other than that, there were some peripheral differences like the cartridge and controller ports, but these would not relate to your question.

To my knowledge, there is no NES game that wouldn't run on the Famicom or vice versa (except the ones that are incompatible with the changed slot design)

While the Famicom was different from the NES, a lot of its internal chips, including the CPU, were the same. in other words, there would be no reason why they would act differently. If you were to recreate the CPU yourself, on the other hand, and didn't keep undocumented opcodes in mind, you may come up with a different result.