I have a great with the tray down below. I am also a bit confused on what the alternative would be. Do you just a tray with no grate over it?
If thats so the only advantage I see to the grate is that most of the junk falls through rather than gathering at the bottom of the cage. Some might say that letting your bird scurry through all their own mess may not be healthy. I think there'd be a lot of problems to that argument though: At least my Auggie is hardly ever on the bottom of his cage - he's on a perch, in his hut, or climbing on the walls. Though in my case I have an ENORMOUS cage for him which may be why he doesn't go on the bottom. The other problem with the "sanitation" argument is that when Auggie is out playing he often goes under the grate to get to all the stuff he's dropped in the tray, like pieces of peanuts...
As far as ease of cleaning I'd say a grate actually makes it harder; sure I can dump out the tray, but the grate itself gets filthy and its takes a bit of scrubbing from all angles to clean it. In contrast just a tray at the bottom would be easier to wipe off.
Another thought is that some set-ups without grates use any number of bedding materials on the bottom of the cage. Some of these are great, but unfortunately many of the commercially made materials can be harmful if the birds scurry through it kicking up the dust.
With the exception of using the right bedding material in a grateless cage I suspect most of the differences are that of personal taste.