I don’t use my Ko-fi that often so I could be wrong but I think Patreon offers you more options.
You can create different tiers, adjust how much each tier costs, adjust when patrons face fees. You can upload different forms of content on your page, not just images (backgrounds/overlays) but other things too if you so choose. You can title your posts, add descriptions, people can like the posts and comment. There’s also plenty of space for you to add your terms and conditions.
Although the good thing about Ko-fi is that they can pay you whatever it is you’re asking for (1 coffee, 2 coffees?) and then you can give them access to your backgrounds without them having to make a monthly subscription whereas with Patreon, patrons are more or less expected to pay a monthly fee (they can cancel at any time though) but their access is revoked upon cancellation, it might vary a bit though depending on your settings.
I think with Ko-fi you might have to have your backgrounds on another platform e.g Google Drive, I don’t think you can upload them onto your page in such a way that only those who have paid can see them unlike Patreon. I could be wrong though.
I’m sure others could give you more details and a better insight though. I haven’t explored Patreon in depth, I’ve just used it a lot more than Ko-fi. 🤷
They’d both have their pros and cons, but I’d say Patreon is definitely more geared towards new updates and monthly subscriptions, and Ko-fi seems to be geared more towards donations and/or one-off payments.