interconnects vs speaker cables vs power cords - which make the biggest difference?

IME power cables made the most difference

 It really depends on the system. But in general, power cords and conditioners make the biggest difference. Then speaker cables and lastly interconnects. But again it depends on the system. I have found mixing brands of speaker cables and interconnects can deter the performance of both. Synergy is the most important thing. There is no perfect or best  cable for everyone.

Like your entire system, it's a chain. Changing any one thing will change the system. So you might hear the most difference with any one of these depending on your system.
While speakers (most people think) will change your sound the most, I have always felt that the preamp is the heart of the system. Everything goes through it and if it has faults, they will be passed on to the speakers no matter how good they are.
So, if everything in your system is equal (and this is seldom the case), power cords and power conditioners could make the biggest difference as long as they are of equal to or of higher performance as the rest of the system. Then I would upgrade the speaker cables, so that I know the best signal from my amp is getting to the speakers. And finally, I would upgrade the interconnects to make sure all my source components are sending the best they can through the system.
Some people have good luck with mix and match, but my best results have come from using all of one brand of cables in my system (YMMV).

Just as with everything else in this hobby, you will find no consensus answer to this question. There are many variables, such as system synergy and personal tastes.

That said, personally I have found them to generally work in this priority:
1) Power cords
2) Interconnects
3) Speaker cables

Obviously, YMMV.

Me personally have found power cords will make the biggest improvement (they are the foundation for your entire system) followed by speaker cables and last interconnects. A lot will depend on the level of your system and what level of cables you're looking at.