Padlock in the UNlocked position looking from the front of the box:

Inside the JOBOX, the padlock sits in a carrier and a special bracket is sleeved over the shackle:

The sleeve over the shackle has a hole in it for a bolt in order to keep the shackle stationary:

The lid of the box has 2 big hooks, one in foreground, one in background, and the hooks move up and down in to and out of the area between the shackle and padlock body:

Oh look, instructions inside the lid! A couple of the distances are much more important than the others:

Here is a familiar American Lock Model 5200 US. After I saw how the hooks and padlock interacted, it was obvious that a key retaining padlock would not work:

Here is an Abloy PL330. Same issue with key retaining requiring 2 keys and the keys would have to be left in the box if open at a job site all day long, not great for key security.

Testing proved that a Medeco Metrolock would fit just fine into the recess, but the long shackle version I have was not the correct size for an operational test:

I always knew of these boxes but never quite understood how the padlock actually interacted with the lid in order to lock the container. This simplified doodle explains what is going on inside the JOBOX.

So here's our problem. An American 5200 or an Abloy 330 will not work, or if you do manage to get them to work, the operation of unlocking and locking the box will be very annoying. Most padlocks can be opened, the shackle popped, and the cylinder rotated back to the locked position and key removed. When the user is ready to lock the padlock, they simply push the shackle into the lock body and it snaps shut.
The American 5200 which is usually key retaining and any Abloy padlock will have the following problem. You walk up to the JOBOX, insert key, open padlock, and now your key is stuck in the padlock and you cannot walk over to the OTHER lock to unlock it without first locking up the first padlock you opened. In this scenario, you will never open the JOBOX. If you carry 2 keys with you, then you can open both padlocks, and lift the cover off the JOBOX, but then you have to either leave the keys in the padlocks all day at the worksite, or remove them which requires locking the padlocks. At the end of the work day, you simply cannot close the cover and push the padlock bodies so they engage their shackles, because they are already closed so the cover won't even close all the way because the 2 hooks cannot go down far enough. So now you have to get your 2 keys out, open both padlocks, close the cover and lock both padlocks.
In a padlock like the Master No.5 or the American Series 50 which are both recommended on the inside instruction decal, they key is not retained, so a user can open padlock 1, remove key, open padlock 2, remove key, and open the lid of the box. At the end of the workday close the lid, and push both padlocks deep enough so they engage the shackle and click shut.
As you can see above, I tried to see if a Medeco Metrolock would fit inside the recess and it does, but you would have to make sure that the one you order is non key retaining and check if the proper size shackle is available to work within the dimensions set fourth in on the instruction decal.
I agree with the other users' sentiment that American Lock cylinders with their serrated pins are difficult to pick, but if you are really hard core, get an American Lock padlock with a Medeco core. The padlock will be longer than the Master No.5 or the American Series 50, and will be flush when locked, and it will stick out .75 inches when in the unlocked position while the cover is open. The advantage to getting the Medeco cored American is in case you do not fully trust someone on your day shift who has access to the Master or American key, you can rest easy knowing they're not making a copy at Home Depot on their lunch break, and if they give the keys back at the end of the day, you know that you have them all and nobody is coming back later that night to burn you by taking all the nice tools.
I think that covers everything, if you have any other questions, feel free, otherwise, visit your local locksmith shop and do come back and tell us or show us your new padlocks. Oh, ask for KA (keyed alike) padlocks, so 1 key can open both in the morning instead of fumbling for the other key.
Squelchtone