I apologize for the novel. I'm a bit of a hockey nerd, so this hit me right in the sweet spot.
This is only partially true. American prospects have a few options following their draft year: 1) college 2) OHL (Europe is obviously another option, but that hasn't been a popular choice for most outside of Matthews).
Many of the best American born players chose option 1, played one year, and then went pro; players like Eichel, Gaudreau, Makar (he played at UMass for 2 years), etc. fall into this category. I'd say the primary driver to choose the NCAA route for most players who were drafted/NHL prospects is a lack of overall size and/or strength. Their schedule is far less taxing/time consuming. Games are usually played back to back over on the weekends, and the regular season consists of anywhere from 35-40 games. This gives the player more time to get bigger, stronger, etc.
The CHL is the prevalent league(s), consisting of the OHL, WHL, and QJMHL, for prospects in Canada. The demos of this league skew heavy Canadian, but players more and more players from Europe have been coming over in recent years. The CHL has by far the most drafted players out of any North American league in part because they simply have a much larger talent pool (for both players and coaching). These leagues have a more arduous schedule where teams play 68 regular season games with additional playoff series for teams that qualify. Obviously, a longer season with more traveling would make it more difficult for players to train in season. A couple important things to note for prospects that play in the CHL: 1) if you play in the CHL, then you will be ineligible to play in the NCAA and 2) the CHL and NHL have an agreement that if you played in the CHL for your draft year, then you are prohibited from playing in the AHL until your age 20 season. The NCAA and professional European leagues do not have that same stipulation.
The Europe route is far less common mainly because most draft eligible prospects just aren't physically developed enough to play over there. The KHL, SHL, and even the National League (Switzerlands pro league where McTavish played last year) all employ men, some of whom formerly played in the NHL. While the players drafted in the first round may have more skill than most of those professional players, that skill doesn't outweigh the sheer size and speed difference that the professional players have.
Basically it comes down to a two, main different factors.
Nationality: Are you American? If so, you'll most likely be going down the USNDT > USHL > NCAA route. If you're Canadian, then you're looking at one of the CHL leagues.
Maturity (in terms of body development and overall skill): the bigger and better you are, the more likely that you would choose the OHL or, in rare instances, a professional European league.