It highly depends on what you're doing, what hardware and drivers you're running on.
Now as a note there are three types of API.
Metal, Wrapper and Abstraction.
Metal APIs (or Close-to-Metal) like Vulkan are API that your commands are giving your hardware a list of commands of what you want it to do and when. This is like communicating "Directly" (or as directly as you can without using Assembler)
Wrapper APIs like OpenGL are API which uses common phrases that are then translated to what the hardware understands. This is like using a Translator to get across what you said.
Abstraction APIs like DirectX 5 - 11, are API that you're more giving a general request to what you want to happen; then there is a middle-manager who interprets what you want into list of commands to get close to what you requested.
So, with Vulkan if you wanted a Cube; you'd precisely describe the cube, where and how to render it.
With OpenGL; you'd just describe the Cube...
With DirectX you'd just say you wanted something that looks like a Cube.
In this way, while Vulkan makes sense for developers who want to get their hands dirty... essentially building their own engine., when it comes to a middleware engine that has to be more broad with how it handles things; well then there end up being a few scenarios where Vulkan will outperform OpenGL; as OpenGL by it' nature is just a bit more broad in how it handles things.
If you have LOTS of Objects (Sprites, Mesh, etc.) or you're heavily relying on Shaders; that's where you'll see Vulkan shine in performance... although don't expect to see MASSIVE gains., we're talking maybe 25% (best case) at least with AGK.
OpenGL is going to shine when you have less going on., as well it has less that needs to happen each frame just to tick over.