Most tutorials I've seen suggest acrylic paint for fursuit eyes. I had never seen anyone suggest acryla-gouache paint, but with its vivid colors and thinner consistency, I thought I'd experiment with it.
I also tried two different base materials: buckram ordered from FursuitSupplies, and 18 ct Aida cloth from a craft store.

One disclaimer is: the base colors available to me weren't exactly the same. The gouache set had a lemon yellow, while my acrylic set had more of a golden yellow. So merely in terms of hues on the final result, I attribute the difference to that, rather than the type of paint itself.
On to the comparison!
Paint types:
The two paints act a little differently in how you apply them, regardless of the substrate. Acrylic is pretty much immovable after it dries. Acryla-gouache doesn't reactivate like gouache does (please do not use full-on gouache for your fursuit eyes), but I still had to wait in between the base coat, and the second coat where I added more contrast. So time is a bit of a factor on the painting part.
However, the acryla-gouache ended up saving me time in terms of refining my work afterward. Its thinner consistency I can spend less time poking the holes back into the mesh after the paint dries... which is probably my least favorite part of making eyes. And I want to move on to the fun stuff!
Mesh types:
On the Aida cloth, it was easier to get bright colors and crisp lines. On the buckram, it all blended together a bit for both types of paint.
One disadvantage of the Aida cloth was that it buckled and warped a lot more as I painted it than the buckram did. Re-flattening it during and after the painting process took some extra effort, but not enough that I would consider it a deal-breaker.
Vision-wise, the Aida cloth won out. I could see details and even read somewhat through it. Meanwhile, through the buckram, everything was super blurry.
Overall, the Aida cloth and acryla-gouache combo won me over. Acrylic paint is probably more popular, easily accessible and affordable with the majority of fursuit makers. But being a painting nerd, I had to try out a more niche brand of paint, and I'm glad I did. Similarly, buckram is easier to buy in bulk and seems to come to mind more readily, but after seeing how much more effort the buckram took for less desirable results, I don't think I would go back to using it.
Would be curious to know if any other makers have tried comparisons like this, or have thought to use acryla-gouache for their eyes!
