Either way is used in common speech. If you really want to choose one over the other, try thinking about the antonyms (opposites) of "better" and "more."
better/worse
more:less
I liked it better the way it was a moment ago = I like it worse now than the way it was a moment ago.
I liked it more the way it was a moment ago = I like it less now than the way it was a moment ago.
If you read the inverted sentences, it is more accurate to say that you like it less now than the way it was a moment before, so "I liked it more..." is a better choice than "I liked it better..." :-)