They fail in different places
A website fails at the beginning: it has to be found, it has to load, and it has to look like somewhere it is safe to type a card number. Each of those is a filter, and a small shop loses people at all three before anyone sees a product.
A Mini App skips all three, because it opens inside a conversation that already has your name on it. The trust question was answered before the shop opened, by the fact that the buyer was already talking to you.
A Mini App fails at the beginning too, differently: nobody finds it in a search engine. If your customers come from search, that is the whole argument and you need a website.
Where your buyers actually come from
This decides it, and you already know the answer. If most orders start as a message in a channel, a group or a direct chat, the shop belongs in the chat. If most start as a search, the shop belongs on the open web.
Many small sellers are the first case and build for the second, because a website is what a shop is supposed to look like. Then they spend a year trying to send their own community to a page the community did not ask for.
A quick test: look at your last twenty orders and write down where the first message came from. That list is the answer, and it is more reliable than any advice about what shops need.
What each costs to keep
A website costs a domain, hosting, and the afternoon a year when something breaks, plus whatever theme or plugin you have to keep current. None of that is expensive on its own. It is the maintenance attention that costs, and a one-person shop has a fixed amount of that.
A Mini App costs the plan and nothing else: no domain, no certificate, and no separate checkout page to maintain. The free plan carries 10 products, 150 orders a month and one storefront, which is a real test rather than a demo, and the next tier is $19/mo.
What each does to the buying step
On a website the buyer types an address, an email, and card details into a form they have not seen before. On a Mini App they are already identified by the account they are chatting from, so the order arrives with their name and handle attached and there is one fewer form to abandon.
The trade is that the money moves differently. Mini App orders are seller-fulfilled by default, so payment happens between you and the buyer unless you connect card payments on a paid plan with your own bot, in which case the money goes to your own Stripe account.
The honest limits of a Mini App
It lives in Telegram, so a customer who is not on Telegram cannot use it. It will not bring you search traffic, and it will not rank for anything. And it looks like Telegram, which is a benefit for trust and a constraint if your brand depends on a particular visual world.
Those are the trades, and they are worth stating before you pick rather than discovering in month three.
You can run both
Nothing stops a shop having a website for search and a Mini App for the people already in the chat. They are not competing for the same buyer.
The mistake is building the website first and telling the people in the chat to go and find it. Serve the buyers you already have where they already are, then build for the ones you do not have yet.