On-close orders might be quicker and more automatic I suppose especially for those who REALLY want to wait until 4:00 PM to see what the closing price and then trade on that. Whether to use limit would, like I said before, depend on how desperate you want to get in on the position or close the position.
Another advantage of MOC orders is the ability to trade huge size without impacting the market too much. Depending in the stock and the imbalance a few 100K shares in one go isn't unusual.
With some of the closing prices I've seen over the years, you are rolling the dice with MOC orders. LOC for me.
With LOC orders you are also rolling the dice. How do you know what a good limit price is 10 minutes before the close?
With a limit order you limit the risk, you can only get executed at a certain price or better. With market order the slippage could be limitless, however the close attracts the most volume of the day so that rarely happens. That is why i asked for a crazy close example, i have heard other people mention this as a reason to avoid MOC, but nobody ever could give me an example and in the years that i have been trading i never seen one on the shares i have been trading myself. It will probably happen, but only on stocks with very limited volume.
I've seen plenty of examples of closing prices where it is absurdly off the action just one minute before. If you are really interested, run through some historical data to find some examples. I don't understand why you would ever put in a MOC order when you could put in a LOC order with a price that you would consider acceptable. But I'm glad that you haven't been taken to the woodshed on a closing price yet.
Indeed i haven't and i never have seen an example either, i could probably find some but not in stocks that have decent volume. MOC's are used by many traders and institutions and there is a reason why. Even better, use D quote orders.