Is there a difference between connecting the input of a logic gate to the anode or cathode of LED
You have made "life hard on yourself" by not simplifying the circuits such that it is easier to see what their difference is.

I have re-drawn your circuits, they are exactly the same circuits as yours. But don't take my word for it, check that yourself!







simulate this circuit &ndash; Schematic created using CircuitLab

Now note how the only difference is in the way that the input of the AND gate is connected.

From the LEDs point of view, the circuits are the same. Each LED is directly in parallel with the input voltage source.

Do realize that this circuit doesn't "do" much. LEDs always need a series resistor. Also LEDs need more than 1 V to light up.

Your question doesn't make much sense either, don't think of connecting the input of the logic gate to anode or cathode, think of it in terms of connecting to supply voltage or ground.