Is the Mint building or hunting more effective?

With all applicable workshop upgrades [Edit: Everything up to Hunting Armour, as that's all that existed when I wrote this answer] (which you should be able to get before getting a Mint), hunting once produces an average of 131 furs, 40.5 ivory and 0.04 unicorns. (There's also a chance of gold in Iron Will mode, but I'll ignore that for now.) Mint productivity, on the other hand, is dependent on your maximum catpower. From the wiki:

• Catpower per Tick: -0.75
• Gold per Tick: -0.005
• Furs per Tick: +0.00875% of Maximum Catpower
• Ivory per Tick: +0.00210% of Maximum Catpower

100 catpower (the same amount of catpower it takes to hunt once) is thus converted to (1.1667% of maximum Catpower) furs and (0.28% of Maximum Catpower) ivory, at the cost of 0.667 gold.

Mints becomes a more effective use of catpower than hunting at the following values:

For furs: 11229 maximum catpower

For ivory: 14465 maximum catpower

Note that mints also consume a small amount of gold, and have no chance of producing unicorns. Unicorns probably don't matter so much, since you're likely to have acquired two unicorns and gotten proper unicorn production started by the time you build a mint, but the gold consumption might be a good reason to turn off your mints at times even with very high catpower.

Generally speaking, your most efficient strategy for most of the game will be to turn your mints off when you're actively paying attention to the game, and turn them on when you're about to walk away, or even do something else for a few minutes. Catpower caps out extremely quickly, and mints are the only way to get any meaningful amount of value from the catpower generated while the game is idling.

It depends on a playstyle.

Mints are designed as a supplementary structures for players that want a legitimate way to autohunt. Manual hunting is almost 10x as effective in terms of catpower/gold conversion.

Someone did the calculations on Reddit. To summarize, it is based on how much catpower you have vs how much your hunters are bringing in. For mints to more be powerful than manually hunting:

Fur

• No Upgrades: 3,386
• Bolas : 6,129
• Hunting Armour: 11,700
• Steel Armour: 13,136
• Alloy Armour: 14,486
• Nanosuits: 15,922

Ivory

• No Upgrades: 3,850
• Bolas : 7,229
• Hunting Armour: 15,000
• Steel Armour: 17,122
• Alloy Armour: 19,315
• Nanosuits: 21,579

For anything less than this, you can have maximum hunting effectiveness by using autoclickers.

If you don't like autoclickers, you can get the optimum balance by only partially using Mints. For example, my catpower is about 8k. I have 9 hunters and use 5 mints to get catpower capped every 45 minutes. This is a slow enough rate that I don't have to worry about clicking it every 5 minutes.