Is it difficult to make a béchamel sauce for 15 persons? Is the process different than preparing 2 or 3 servings, and how can I have it come out the same?
I've worked in more than a few commercial kitchens, and we've always made 'mother' sauces in large batches during prep for dinner. Béchamel is one of them; it's the base to quite a few other sauces.
For 15 people, I'd suggest using a small stock pot with a thick bottom on medium-low heat to cook out the roux, and then use the residual heat to hold the sauce if that's how you plan to serve it. Cook the sauce just prior to serving it.
Just remember, the more of it you have, the heavier it gets, and greater pressure is exerted on the flour at the bottom of the pot. Once you think it's nearly done, use a ladle to pour some into a shallow bowl, do the spatula test as Joe suggests and get it off the heat as soon as your happy with it. And, whisk from the bottom up (a figure-8 as you turn the pot works well, and turning the pot helps prevent burning). Otherwise the last few servings are going to taste a bit off.
You can also use a wide but more shallow pan, which also reduces the risk of burning some of the sauce. I've just not yet developed the amount of control over my enthusiastic whisking problem to do that in a setting where I'm also responsible for the mess :)
The only trick that I can think of when dealing with larger batches of béchamel is to use a wider pan on your widest burner.
This gives you more space for spreading out the roux, so that you get it more evenly cooked. It reduces the amount of stirring required by minimizing the temperature gradient -- you can keep the temperature lower so you don't risk overheating the stuff at the bottom.
I also find it easier when adding the milk, as I can more easily tell when I have it well incorporated and when it's reached my desired consistency (drag a spatula through the middle to leave a clean path, and see how quickly it fills in)
Note that I use a wooden spatula; it's possible that you might want a taller vessel if you're using a whisk to minimize splashing, but then you're going to have to spend more time stirring.