The short answer to your question is yes, they do work a lot better than a bench plane on its side. I have one, and dozens of other planes besides (that I could use on a shooting board), but this is my go-to for end grain."Do these things work a whole lot better, (like $375.00) better than a regular plane on its side? Let's just say you had the cash burning a hole in your pocket, is it something you would get?"
There's a couple of reasons for this - the large, perfectly 90 degree side on the plane makes a very stable platform for running on the bed of a shooting board, and the "hot dog" handle makes holding the plane square to the end of the board considerably easier than gripping the thin side wall of a bench plane. By the way - the side handle Dominic shows in his picture was an earlier version of the #9 - they were shipped both with that handle and an optional "hot dog". The current version deletes the side knob and is shipped with the hot dog handle as standard equipment. If you've an older version that did not include the hot dog, you can order one from L-N and it will fit.
So - I would heartily recommend the L-N #9, but as the other posters have noted, you should be able to get a standard bench plane to work on a shooting board. If you can't, it's likely to be the sharpness of the blade, too big of a cut, or too hard of a wood. To start with, you should practice with something soft like eastern white pine, poplar, aspen, etc... The end grain of something like maple or walnut is really hard, and you should graduate to these woods, not start with them.
Finally - I tend to stay out of the Lie-Nielsen/Lee Valley debates, because I think it's a preference with no clear winner, and saving less than $100 dollars on a tool that you'll spend your lifetime using is not a justification for picking one brand or another (the Lee Valleys tend to be cheaper, with the difference depending on the model). Nor do I think it's a good idea to have just a couple of planes and a bunch of interchangeable blades (and you can do that with either L-N or Lee Valley bevel up or bevel down planes).
However, this is one instance where the Lie-Nielsen low angle jack plane might offer a significant advantage - a hot dog handle can be ordered with the plane, and that makes using it as a shoot-board plane a lot easier.
My personal preference, of course, is the #9, but if you don't already have a jack plane, you may well be better off by buying a bevel up jack (of either brand).