Sometimes, someone slightly more aware of the situation might ask something in the direction of "straight out of the camera, which one has more vivid reds?" This is a question that makes slightly more sense to ask, but only just.
|Nikon or Canon?|
As I have mentioned here and here, any modern DSLR can be tuned (not to mention, its RAW files can be fine-tuned after the fact) to produce results identical or at least very, very similar to any other DSLR of the same generation. Which means, if you like the output of your friend's Canon, it is trivial to adjust your (let's say, Nikon) camera in a way that matches that output. If you can't, it means something else is to blame and not a Nikon-versus-Canon thing.
Let's take a look at this in more detail.
The technical things that affect the output of your image:
2. Curve settings (for the layperson: "contrast & brightness")
3. Color settings (saturation)
4. White balance
That's all, folks. As long as we're not comparing apples to oranges, (comparing a contemporary Nikon D500 with a Canon EOS 350D from the year 2005 isn't exactly fair), then you'll notice very little if any difference between, say, a Nikon D5500 and a Canon 750D. That is, you might notice very little or no difference when shooting jpegs.
What if you're shooting RAW?
Well, then you will notice no difference. First of all, items 2, 3, and 4 above are adjustable after the fact. Did you shoot a portrait in "vivid" setting? No problem, you can reduce saturation and adjust the curves after-the-fact. Dislike the Auto setting of the white balance? Again, you can fine-tune it. I hope you're beginning to see why the whole Nikon vs Canon thing becomes irrelevant when shooting RAW, but I'd be glad to spell it out for any beginners out there: when shooting RAW, and when you adjust the curve, the color, and the WB yourself, any "factory settings" regarding these things cease to exist. Hence, any minute difference between the way Canon engineers and Nikon engineers program their "Portrait" preset, goes out of the window.
Which leaves us with exposure. I've talked about it before, and you ought to read that article carefully. Understanding how to control exposure will make everything else fall into place almost magically.
Perhaps I should conclude this article with a few pictures - three pairs, to be exact, depicting the same scene. Some are taken with a Nikon D3200, some with a Canon 450D (not exactly a fair comparison, but close enough). Wanna try to guess which photo is taken by which camera?