I've had one of those Gator type plastic storage boxes mounted on the front of my 18' trailer for 15 years. It wasn't waterproof. I added that stick on grey foam to the channel on the underside of the lid that the top edge of the sides go into and have a couple holes drilled in the bottom. I keep a winch (and it's accessories), gloves, tie downs, wheel chocks, tire iron, moving quilt, etc. in there, and it's not under a hood but out on the A frame part of the trailer just behind the coupler.
I think unless you purposely spray down the cheaper box from the sides with a hose or high pressure wand it'd keep out most of the water.
Those expensive sealed battery boxes are for when the battery is placed inside the passenger compartment, like in a race car, and needs to keep gasses or acid in (well, they usually have a vent which is vented to outside the vehicle) and they need to pass tech inspection at a track.