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The better option is just use a wallet which have RBF feature, so whenever you're need it but the transaction still not confirmed yet, you can bump the fee whenever you want.
Unfortunately, many of those who do BTC transactions have never heard of something called RBF (replace by fee), and even if they have, they still have a problem because they use online wallets (CEX) that do not have this option. For beginners, such things can be quite confusing, but as I saw on the forum, even for some older members.
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Same fee can be used to send big amount of Bitcoin or smaller amount, all depends on how busy the network is at that point of transacting. If the network is congested then you might want to increase your fees to get a faster transaction.
It is true that the fee may be the same, but still the total price of the transaction depends on the size of the transaction. For example, you can make a transaction in which you send 0.10 BTC to one user, and that transaction will have one input and two outputs (recipient+change address) and let's say you will pay a fee of $1. In the second case, someone can also send the same amount of BTC, but the difference will be more inputs (address from which BTC will be sent) and more outputs, i.e. multiple recipients.
The first and second transactions will undoubtedly be different in size, which means that the second transaction will be more expensive than the first, regardless of the fact that they use the same fee.