Aesthetics is in the same position (lack of grounds) as morals, except that aesthetics is worse in that there is far less agreement than in morals.
Just because not everybody agrees about everything doesn't mean you can't have objective criteria for making judgements.
The Arnold poem is aesthetically more pleasing because of its more successful use of metre and rhyme. It's a really simple, physical thing and you don't need to be a literary critic to feel it. Read those two poems out loud and 99 out of a 100 people will laugh at the second poem because its metre and rhyme are inappropriate. Even people with no literary education are brought up with nursery rhymes and songs, so we all have at least this much feeling for poetry.
If I'd chosen a poem by ee cummings to compare with Dover Beach, making aesthetic judgements would have been more difficult and possibly would have been beyond anyone who didn't have a literary education. But even then it's possible to make
objective judgements. After all that is what literary criticism is about - it's not about saying whether you like or dislike a poem (which is always going to be a subjective thing, based on your own experience of life, your own tastes and preferences) but about the objective aesthetic effect of a poem.
There is a great deal of ridiculousness in Shakespeare--and in Arnold, too, for that matter.
What do you mean by
ridiculousness? If you mean bad poetry, why does that reflect on our judgement of the good poetry?
The true mystery of the world is the visible, not the invisible