I think initially it was a matter of style... MTBer just wouldn't be seen in those bright colors lycra kits. They wanted to appear to be an "alternative" culture. Their shorts were baggy and shirts were baggy just to be different from rode riders.

Of course, I now see bright colored roadie kits on lots of mountain bikers. I wear what's clean, having more road shorts than MTB baggies but I have to say there is a real functional difference. Now I do have one complaint about most women's MTB shorts - they are so short as to make no difference and offer no protection (most coming just a few inches below my hips). Because I'm tall, I buy and wear men's shorts. They usually hit me around the knee.

In California, springtime is thistle season. Those baggier, sturdier shorts difinitely protect my legs against the thistles and stinging nettles. Also, just recently I had flats on my MTB bikes. It's goathead thorn season. Had to sit in the dirt (and in the thorns or rocks) to repair the tires. Both times I was wearing Lycra. Learned a lesson; from now on I'm wearing MTB shorts. Much better protection for my bum!!!

Road shorts usually have a better chamois but that goes along with function. If road riding I sit constantly on the saddle. While MTBing I'm up
and down alot so the chamois isn't really an issue. In fact, the lighter the better.

Hope that answers your question.