You are correct in stating that there are no significant differences between the two. But a huge heap of minor differences do add up to two different characters of cameras--either one of which could easily suit your needs. Any statements about how different the two makes are as broad generalizations will typically be wrong--there are going to be exceptions on either side. Which system might be a better fit does come down to individual usage, gear needs, and feel-in-the-hands.
But here goes.
When it comes to wide angle shooting, Nikon typically offers more lens choices, particularly for a crop shooter. Canon has no 10.5mm fisheye for crop, nor a cheap fast "normal-on-crop" prime, like the Nikon 35/1.8. And the Nikon full-frame pro-quality 14-24/2.8 is without peer. When it comes to supertelephoto (>300mm lenses), Canon offers a few more mid-grade and lower-priced choices. For example, Canon has a 400/5.6, 400/4, and 400/2.8 at $1400, $6500, and $11,500 price points, while Nikon only offers 400/2.8 primes a the $9000, and $12,000 price points (OTOH, Canon's 100-400 zoom and Nikon's 80-400 zoom are both around the same price). Canon has an additional 17mm tilt-shift lens.
So, there is a lens give-and-take between the systems, and which one will suit you better depends on which lenses you actually need. IF you don't need a 400/4 prime or a 17mm tilt-shift (and few people do), then the absence or presence of one hardly matters. And, of course, there are often 3rd-party lenses to fill the gaps.
Low-end body "crippling"
Nikon's low-end bodies (D3x00 and D5x00 lines), arguably, suffer more from "dumbing down" than Canon's low-end bodies (XXXXD and XXXD lines). And Canon's recently added one additional dRebel line with dual wheel controls and a top LCD. Again, whether or not you need these "gracenote" features will determine whether it matters. Low-end Nikon bodies do not have a DoF preview button, cannot do true mirror lock-up, do not do high-speed sync flash, and may not have autobracketing as a feature. All of these features exist in the lowest-end Canon dSLR bodies, but they are more expensive.
Where there is a larger "missed" feature, however, is that Nikon low-end bodies do not have focus motors in them, and Nikon does not put focus motors in all of its lenses. And you need one focus motor somewhere to perform autofocusing. The practical upshot of this is that if you purchase a D3x00 or D5x00 body, and use an AF (not AF-S) lens on it, that lens will not autofocus. Nikon is the only brand with this specific issue. Most Nikon lenses are now AF-S, so this is far less of an issue than it was, say, five years ago. And, of course, not all subjects require autofocus.
On the flip side, all the film-era Nikon F-mount lenses can still be used on a Nikon body, while Canon's FD/FL manual focus lenses cannot be used on an EOS mount directly.
As with the lenses, Nikon tends to engineer for backwards compatibility, while Canon tends to go more bleeding edge and makes its older gear non-compatible. Another pithy way it's been put is that Nikons are designed by photographers while Canons are designed by engineers. Which one will be a closer design aesthetic to your personal tastes is up to you. But depending on the age of gear you might have inherited or that you can borrow, this might make a difference.
Left-to-Right vs. Right-to-Left
A minor note: Nikon tends to go widdershins while Canon doesn't. Lenses mount counter-clockwise, and the exposure scale/meter (unless you change a setting in the camera) by default puts -EV on the right, and +EV on the left. Canons, otoh, do the lefty-loosy, righty-tighty thing with the lens mount, and puts -EV on the left and +EV on the right.
Canons seem to have a disproportionately larger number of engineers using them. And many of those engineers happen to write firmware in their day jobs. The result is that some very talented people looked at the CHDK, looked at their dSLRS, rolled up their sleeves and went to work. Magic Lantern exists for some Canon dSLR models, and works quite well to add some frankly astounding features that Canon hasn't seen fit to add, such as focus-peaking, a built-in intervalometer, single-shot HDR, auto-ETTR, video HDR, trap focus, etc.
Nikon hacking is undergoing, but has not reached the level of Magic Lantern in terms of code maturity.
For a while, Nikon's CLS wireless flash system was far more convenient than Canon's, because Nikon built CLS masters into the pop-up flashes of its prosumer camera bodies, and Canon didn't. From 2012 onwards, however, Canon has begun to add this feature into its bodies, and even down into the XXXD dRebel models (600D forward all have this feature). The lowest-end model Nikon has this in is the D90/D7x00 tier.
However, the Nikon mid-grade flash, the SB-700 is arguably a higher-end model than Canon's mid-grade flash, the 430EX III-RT, as it has master capability for wireless control of another flash, and includes SU-4 mode ("dumb" optical slave capability). Neither model, however, has a PC sync port. And the 430EX III-RT has radio control and the additional wireless features of the RT system.
In 2012, Canon added built-in radio control to its line of speedlights with the 600EX-RT (although there are no built-in radio masters in the camera bodies--you need another 600EX-RT or an ST-E3-RT to perform that role) and followed up with the 430EX III-RT. 3rd party manufacturers have, in the time since, created compatible flashes and triggers with the Canon RT system.
Nikon, otoh, is introducing its first radio flash, the SB-5000, in March of 2016.