In my eyes, over the decades both companies kept leapfrogging over each other. With the T90, Canon probably made the most advanced non-AF SLR, only to abandon the FD-mount. This was a very costy change, which paid of later on, as it allowed Canon to start over without any legacy. Early on, Nikon had the lead in DSLRs, but Canon was the first with a 35mm DSLR. Nikon took a long time to go 35mm, but the D800 and D810 was a big step ahead with its 36mp sensor, only very recently Canon exceeded that with ther 50mp version of the 5D.
The next important step for both companies will be the transition to mirrorless technology. As µFT and the Sony A7/A9 are showing, mirrorless is the next step in camera technology. It will be interesting to watch how Canon and Nikon approach this transition. As both companies currently make their money with SLRs, it is a risky step, but an inevitable one. If one of them missteps in that transition, it means at least a big set back if not a complete loss of their role in the camera market.