In the early game
Woodcutters win. They're giving you 0.015 wood per game tick, whereas farmers are giving you 1 catnip per tick. In a hundred ticks, the farmer has earned you one wood, whereas the woodcutter has earned you 1.5.
As you upgrade
The Mineral axes upgrade is +70% wood. Mineral Hoes is only +50% catnip. Iron Axes/Hoes are 50%/30%, and from Steel onward, Hoes aren't getting any more upgrades.
When you get the Catnip Enrichment upgrade
You've probably already got the Mineral/Iron upgrades mentioned above. A hundred ticks of 1.8 catnip is 180 catnip, or the equivalent of 3.6 wood from a farmer. Those same hundred ticks of a woodcutter with Mineral and Iron are worth 2.2 wood. Even Steel only pushes it to 2.7.
However, by this point, you've probably also got Lumber Mills and Aqueducts. Lumber Mills are providing a +10% bonus to wood, Aqueducts a mere +3% to catnip. With Steel Axes, Lumber Mills can quickly put Woodcutters back on top.
Another big reason Woodcutters will tend to win, is storage. This game isn't going to be over in an afternoon; at some point, you're going to start leaving it for a while to build up resources. Your catnip storage is never going to be fifty times your wood storage, so if you plan to leave the game for an hour, it's better to have your kittens working on wood directly; farmers will hit your catnip cap quickly, and need you to manually hit the refine button.
Related to the point about storage, there is an upgrade in the game that allows automating some of the workshop crafting tasks while idle. Every so often, it will craft some of your Wood into Beams, Minerals to Slabs, and with another upgrade, Iron into Plates, as long as your storage of those resources is full. This is great for leaving the game overnight, but one thing it notably doesn't do is refine catnip. By having your kittens working on wood directly, you'll be more likely to have your wood supply back to full every time this effect runs. Additionally, by now, you've potentially gotten the fourth Axes upgrade, as well as the first couple of Saw upgrades that improve your Lumber Mills
So, even with all this, wouldn't it still be better to at least focus on Catnip during the period right after you get Catnip Enrichment, at least while you're actively paying attention and refining? Sadly, no. Because your kittens have skills, and thus get better at a job that they keep working at. Shunting your kittens back and forth means splitting their skill growth, resulting in a population of kittens which take longer getting to Proficient or Master at either job. The bonuses for the last two skill levels are quite impressive (50% for proficient, 75% for Master), so keeping your kittens on the same job is generally a good idea.
Kittens should be made farmers only as needed to keep your population alive. Refining spare catnip won't hurt (unless it'd be better spent on a Catnip Field or Pasture), but the only time you should be focusing heavily on refining catnip, is if you're playing in Iron Will mode.