I don't mean to question your knowledge, just wanted to make sure.
Thanks very much!
Among many ping-pong players, 19mm is often considered the minimum thickness for a good standard table tennis table. My own table is a 19mm Stiga Elite Roller that I've had for many years and it still plays great. However, I've played on thinner Stiga Basic Roller tables and found them to play just as well as far as I was concerned, so just because the table surface is thinner does not mean that the table won't be good to play on. After all, how thick does the table need to be to bounce a 2.7g ball consistently? What are those extra 3mm between the Stiga Basic Roller and Stiga Elite Roller really going to do to the bounce of the ball?
Aside from the play of the table, what you do need to keep in mind is that the thicker playing surfaces will usually resist warping much better than thinner tables. And that the more expensive tables are usually the ones with thicker playing surfaces, so it's entirely possible that more care is taken in their construction, and the quality control on such tables is higher. Mind you, that is only a conjecture on my part.
As far as quickness of the table - that is more an issue regarding the finish of the playing surface rather than the thickness of the table. There is a fair bit of variation in quickness from brand to brand, simply because they have different finishes. A slick, glossy finish is likely to be a fair bit faster than a dull, gritty surface.
In regards to your Prince ping-pong table - if the 15mm version is not so good, the 19mm version is also likely to be not so good. It will resist warping better, but the finish and playability is likely to be fairly similar. I'd recommend sticking with reputable brand names such as Stiga, Butterfly, Joola, Killerspin and DHS. These are the mainstream manufacturers of table tennis equipment for a reason. You may pay a bit more but you you will certain to get a decent table for your money.