There are a few similarities when you think about it but of course there are always exceptions. So here goes.

1.Memory: When you get really drunk you have a lower degree of awareness and on the next day you might find hard to recall what happened or maybe not even recall what happened at all At the very least some things may be fuzzy. In a non lucid you have a much lower degree of awareness than usual and once you return to waking life you may find it difficult to recall what happened (of course if you worked on dream recall then this problem is not as bad as I make this sound but like I said, some details can be fuzzy).

2.Lowered prohibitions: While really drunk you may do things that you wouldn't do when you were sober. Similarly in a non lucid you may also do things that you would not do in waking life like beat someone up, and have sex with some girl you find sexy, etc. (Lol generic examples)

3.Dulled senses: While drunk your senses are not as keen as they would be if you were sober. In a non lucid dream you can see and hear but as far as touch, taste and smell goes, those senses are almost non existent in a non lucid. (Of course there are always exceptions. I didn't say it was impossible to perceive those senses, just saying that they are usually dulled down in a non lucid.)

And that is all I can think of. Anyway I am not saying that what is listed above is absolute, there are always exceptions. List other example if you want.