Bandcamp doesn't have a real cart so if your browser cookies are lost the cart is gone (and you can't login from a different device or browser/container and see the same cart). If you add too much music to your cart at once it breaks and the entire site doesn't work until you clear the cookies (messaging customer support they were just like "oh yeah, that happens"; I haven't checked recently but I bet it is still like that). Hopefully you kept a window open with a nearly full list of what you wanted to buy or it is gone. I've seen Bandcamp developers post on hiring threads where they actually seem proud of their horribly broken system.
Back when Paypal was charging extortionate fees for currency conversion (if you didn't manually convert paypal wallet funds yourself) the conversion rate that Bandcamp showed was way lower than what Paypal actually charged (I think it is still a bit lower after Paypal agreed to charge less after getting sued). Trying to avoid using a Paypal account and use a credit card the many charges that Bandcamp makes always sets off the fraud alert on my credit card and even after I say it is ok and try to finish the transaction it seems to have trouble. Last Bandcamp Friday the 20ish minutes I left to attempt to pay them wasn't enough. There is no Bandcamp wallet while the GOG wallet is super convenient (and GOG has payment options that don't go through Paypal at all). Also the gift code system on GOG, other than the annoying captchas (which Bandcamp has every time you sign in) is really great and you can see if a gift code was redeemed and give it to someone else if not. On Bandcamp it is hard to tell if a gift was redeemed and as far as I know you can't give it to someone else if the person you bought it for doesn't want it. Refunds on Bandcamp are done by the artist in most cases as I understand it (since you can fully listen to most of the music there is less need for refunds in general).
I forget if you at least get the opportunity to make your account private when you first sign up but you can't make it private later (I just noticed that you can make your wishlist private and hide individual albums from your collection). I dislike the idea that everything I buy is made public although I wouldn't mind being able to show stuff that I most recommend (I'd like it to be default private). GOG doesn't have a good way to just show what you recommend but at least you can change privacy settings.
The wishlist on Bandcamp can't be shown in text list form or sorted in any way (other than the default time added) and it doesn't show the price (I can to some extent understand them not wanting to encourage purchases based on price but it is an issue when some stuff is most expensive than most; a way to make multiple wishlists would be helpful there and here). You can't follow an artist on the website but not receive email from just some artists, you accept email of particular types from everyone or no one. (I guess to be fair you can't follow developers or publishers at all on GOG, which would be a good addition). GOG's website works better with a minimum font size set (maybe partly because I bugged them about it when the download links didn't work correctly; I didn't try to contact Bandcamp after how they responded to trouble trying to actually buy things).
Bandcamp isn't really clear that stuff can disappear from your account if the music is removed from Bandcamp. Some of the FLAC files are obviously converted from lossy formats and they almost never tell you this. 7digital is honest about these things but unfortunately unlike Bandcamp they are heavily regionally restricted (and have much less indie music).
That is what I can think of right now at least, I might be forgetting a few things :/. I haven't used the mobile app.
Edit: oh yeah, there was another payment issue where going to Paypal and then returning to Bandcamp would mess up the cart after a few times and again the cart needed to be cleared and refilled.
