It’s complicated. The best I can say is that the Oil’s are technically better, but only under certain situations.
The Oil of Bounty will add +10 harvesting power to whatever tool you place it on. So, your +12 becomes +22, or your +22 becomes +32. Its’ very powerful, but it only lasts for 12 minutes while deployed.
When equipped, the Oil of Bounty starts a timer that counts down from 12:00 minutes. During that time, you can harvest whatever you like for a much larger amount than normal. But after that 12:00 period of time, your tool essentially breaks and needs to be repaired.
The situations this is most useful, is in area’s where there are either rare, or bulk resources you can gather in a short amount of time.
Star Metal would be a good item to use Oil of Bounty on. Crack open the shell, expose the ore. Pull out your tool, pick it a few times. And you have +60 extra ore over what you would normally have, for each star metal node you find. You then unequip the tool so the timer stops counting down. This way, the tool will last you for the duration of your run. You could do it for Brimstone as well, but I feel like there is an awkward amount of running, and swapping the tool on and off. It may not be super efficient… but it will definitely result in a lot of extra brimstone.
My best suggestion, is to use the Oil of Bounty on a tool of your choice. (Black Blood Pick) and go to the silver mine. There you will find a LARGE clump rock early in the dungeon, on the left side. You can hack your way through that and gather a ton of stone… then proceed deeper and do the same thing to Iron and Coal deposits.
Short of things like that, it’s better to just use a regular tool upgrade (and hard worker perk).
Regarding your second question, ALL of the Oil’s are superior to the normal mods, but they come with a timer, that then requires you to use a Legendary Repair kit (or risk accidentally breaking the item) if you are not paying attention.)
I think the +Damage Oil lasts for an hour, or even two. And it gives a substantial boost to the damage of your weapon. It’s actually very nice… but again, situational. As it’s expensive to make, and will require an expensive fix in an hours time use. But the gain you get from it… is negligable in most cases.
My best thought… Maybe fighting the Arena Champion, where putting out extra damage could keep your favorite thrall alive, for example. But again, only works on unmodded weapons.
Oil’s are very situational, and their time varies depending on the oil. I think the shortest Oil is the Oil of Bounty, which lasts for only 12ish minutes.