Not really. Not when I put any thought into it, at least. They seem synonymous.
I suppose--and this is really an "I suppose"--"rise up" as used in that context makes me think a little more of the height of them. "Rise" is essentially indicating that the hills have a higher maximum altitude than where we are. That could mean even just by a few feet (even though I wouldn't read it that way). On the other hand, "rise up" almost makes them intimidating. It rings of "the hills are towering over me," which is a very different feeling.
Although that said, I'm not sure I'd even go that far in my subconscious if I were actually reading that in a real-world situation. Particularly in the context of "lush green hillsides," it's pretty clear that "intimidating" isn't the goal.
On top of that, clearly "rise" implies, if not even means, the same thing, but I think the word "rise" kind of falls to the background when I read it. It reads as filler text, and that's not a bad thing at all of course, but when you explicitly say "rise up," it really jolts me that "hey, this is definitely something I should be paying attention to."
So, yes, when I really think about it, I suppose they do have some discernable qualities. But in reality, I don't think I'd take notice. Especially if they weren't placed together for direct comparison.