When using a framed trapdoor on the upper half of a block, the top of the trapdoor will show the side texture of rotation-specific blocks. When using a framed trapdoor on the lower half of a block, the top of the trapdoor will behave normally and show the top of the block.

i.e. on the top, the bark side of the log would show, however on the bottom, the inside of the log would show.

Ideally, this would be different depending on how you place the block into the trapdoor.

Can you show some pictures? I think I get what you mean though.

Sure: