While I understand that the 777 ADIRU is more advanced then the 737 NG's, I'd still rather have completely independent systems for left and right sides. I just don't trust any single system, regardless of its internal redundancies, to automatically ignore bad inputs and always display the right data. This seems to be borne out by the 787 cases here.
Right from the start of our careers we are taught to trust our instruments, but more and more often, the modern instruments are having simultaneous widespread failures. AF447 was a good example, but that was well after issues with pitot heads had been identified and the accident could have been avoided if the faulty units had been replaced. Now the 787 is getting similar issues. So, do we now have to change mindsets and start second guessing the instruments?
With single source systems, any failure can lead to all displays showing the same error. I don't know if that was a factor in the AF447 accident as I don't know their architecture, but I think that despite its flaws, you have to go a long way to beat the 737's simplicity and redundancy. More modern types seem to have too much networking and too many vulnerabilities to a single fault.