This would be Canon's AI Servo autofocus, which is your choice of continuous servo approach. It is available on all Canon DSLR cameras, to my knowledge. The other two options are Single Shot and AI Focus. In high-end Canon bodies, you have the option of setting one of the rear body buttons to focus. In the newer bodies of Canon, there is usually a dedicated AF-ON button on the back of the camera already set up for this purpose. If you press and hold the AF-ON button (or the button of your choice) when using AI Servo drive mode, you can take continuous shots with focus between frames, subject tracking, etc.
When it comes to subject tracking, the camera can do some of the work, but you must make sure to keep the subject in the frame. You must also ensure that the subject is within an adequate range of active AF points, otherwise the camera will not be able to correctly determine what to focus on or track the subject. The proper technique of continuous / servo AF with subject tracking and focus adjustment between frames requires skill, and like any other skill, must be learned. You will have to put yourself into practice to be able to effectively use any AF system, and the more hours, the better you will get.
As for the highest AF points, it is actually Canon that has 61 points, in its two newest cameras of professional level: the 1D X and the 5D III. The Canon 61pt AF system is, specifically, the best in the world at the moment, with 41 cross-type sensors and 5 cross-type sensors, sensitive up to f / 5.6. The Nikon AF system is 51 points, with 15 types of crosses, whose central group is sensitive up to f / 8, while the rest is f / 5.6. Regarding whether one brand "exceeds" the other, that is truly irrelevant in the grand scheme of things. Both brands regularly outperform each other. At this time, Canon is the king of ISO and AF (many of the first users of the 5D III have been surprised with the capabilities and accuracy of the new AF 61pt system), where Nikon is currently the dynamic range and the Megapixel king. It is unlikely that these factors will remain the same for long, and after the next round of camera launches by both companies, the statistics will undoubtedly change again.
Do not use "who is better" as a factor to buy … that will never end well. Find out what you you want to do, what is your budget, if you want to be able to share glasses with friends that have the same brand as you, etc. The two Nikon cameras used by his friend, the D3s and the D700, are very advanced. Cameras, and they cost a lot of money. Canon has similar cameras, such as 1D X, 5D III, 1D IV, etc. that also cost a fortune. If you are just starting with the picture, it looks too close to the totem, and you might not need a camera like the one that appears at this time. Look at the lower range if you are starting. For Canon, that would be the Rebel series (numbers xxxD), and for Nikon, look at the D3xxx series. Buy a CHEAP camera body, since bodies come and go, and change every two years. The true long-term value in photography is in lenses, and in that area, Canon has a bit of an advantage with a larger selection and some unique entries in its line, as well as some unique designs that no other company uses. In any case, Nikon also manufactures excellent glasses, and you can not go wrong with any of the two brands.