First of all, I much prefer your first dirt. Your second is absolutely disgusting to me!! It looks almost just like a noise. Use it for REALLY pebbly areas, but not as general dirt.

Anyway a large part of fixing the grid really isn't that your tiles are bad, but in how your tiles are laid. We're working with small tiles here, they're almost always going to look tiled unless the colors are really low contrast.

To fix it I simply will just show you a process here:

Your original image. I enlarged the canvas a 16x16 tile on each side for rearranging purposes.

Here you will see that I shifted every other 32x32 row over.

I put the excess tiles in the whole on the left side.

Since we already shifted each 32x32 row, I decided to shift only every other 32x32 column, and only a single 16x16 column of that. Why? Because we've already rearranged drastic rows, only a tad bit needs changed on the columns to add variation.

Here I filled in the games with the excess. It looks great!

If we moved every other 32x32 column (instead of a 16x16 column on every other 32x32 column) then you'll end up with a snazzy dirt ground, too. And this is what it looks like. Whatever floats your boat