I have not personally used the L version, though i know a bit about it. Apart from IS, I believe the L may be sharper at the wider end, but that's by a fraction. With no real world use from me I'm only rephrasing what I've heard about it.
Alright, when I had to choose between L version and non, I decided to go with L because of image stabilisation . As i don’t really carry my tripod with me all the time. But as Yohanna_D mentioned above that you can shoot handheld , than it’s make this lens to be right fit .