It doesn’t matter which one. Just make sure is a proper vector software, that’s all!
One of the key characteristic of a good logo design is its simplicity. (More about good logo characteristics on this article). And you cannot surpass the sharpness and precision of vectors. On top of this, its infinite scalability makes the ideal route to follow when designing a logo.
I’ll do my best to explain this from a logo design perspective that is relevant to what we are discussing. Although there are more thorough and specific definitions out there.
A vector is a visual representation of a mathematical equation. The software reads formula and uses this information to display a graphic. This makes vectors very robust when it comes to scaling up or down to almost any imaginable size.
Industry leader on design. Adobe keeps implementing tools that makes workflow more efficient and practical. It comes with a price though.
The dark horse of design. Affinity keeps improving not only its software but entire ecosystem. And Designer has all the tools you need to create a fantastic logo. Super reliable, good value and no subscriptions.
Great open source app for vector illustration. Has everything you need for logo creation at no cost.
Photoshop or any other photo editing software. Generally speaking software that works with raster images (JPG and PNG) has serious limitation when it comes to the scalability and fidelity of a logo. Best to stick to vectors as a solid rule of thumb.
Simple tip: when requesting final files from your designer, make sure to ask for vector files. These can be files such as PDF, EPS or SVG. Make sure that when you receive the files open any od them and zoom in as much as possible on to the logo, if the details are still sharp and clear, you got yourself a vector logo file. On the other hand, if when zoomed in the image starts to look blurry or pixelated, you might want to rise this up to your designer.