Is there any advantage is setting higher gas-limit (not gasprice --> gas-limit)? I know you have to set at least as much as that the smart contract needs to execute, but isn't this amount always the same?
A mining client can be written to customize which transactions should be selected for mining. The eth_newPendingTransactionFilter method can filter pending transactions based on any of the transaction attributes, including gas limit. So, theoretically, it COULD be a factor. However, I don't think any of the popular mining clients factor in gas limit.
but isn't this amount always the same?
Why would it be the same? The gas limit is specified by the client. If you're writing the client that makes the call, you would either specify your own amount (and hopefully customizing the amount based on the transaction you're invoking), or you're probably using a library that will determine what value to use based on the results from