It's much better, certainly. I think the level could really benefit from having more going on in the background - not necessarily the 'close background' (like the sunflowers and cats) but the 'far background' - hills or trees or something. Just so the player isn't staring at a gradient, basically.
Also, you might want to think about adding a story or some kind of motivation... at the minute there's no real reason to enter the cave other than /because it's there/.
As for more specific level design - it seems pointless to have just one jump that requires the umbrella, and to have the umbrella sitting right there in front of it. Why not just make the jump smaller? A very small error in the screen below that (i.e. the bottom of the waterfall) is on the right edge of the waterfall there's a tile that doesn't match up - possibly on a different layer? I'm not sure. And what's the deal with the shifts out in the plains?
I feel bad for criticising you so much, but you said you wanted to make the level better. Oh, I did like the use of the 'unfinished level' tileset as cave paintings or whatever, that's a clever idea.