There is a game to teach people about the rules in my local GW store this week and I was wondering how similar are the lotr rules to warhammer 40k or fantasy so I can attend and learn about the lotr as well.

In my opinion Lotr is the stand out game of the 3

there are many similarities between Warhammer and 40K.

Lotr has a different turn order, combat style, different wounding charts, less rigidity and less GW support.

I like how Lotr is fast paced and more involved but dislike how shallow the variability between units are.

I agree with your first point and partly with the second. It depends on what race you're playing. But if you mean variety between races, then I agree.
Lotr It is also more cinematic since you control every soldier individually and the terrain tends to be more important. Additionally the rules are less convoluted.

Here is series of videos from girl painting on to play LoTR. http://www.youtube.com/watch?v=_c91CzKT-nE

Enjoy

Thanks! The videos are most helpful