Cross-border payments are more definitely more interesting. There's a lot of complexity that is outside the scope of the standards - research correspondent (nostro/vostro) accounts and cash management, for instance.
Basically, you need to find a path from your bank to the target bank account through the cheapest path of intermediary banks that factors into account fees charged along the path, expected daily transfers at that bank, the payment's impact on liquidity and interest rates of cash left on books in a particular account at a particular time of day vs. alternative options.
The thing about international wire payments is you never know what you will receive. I send out an invoice for X and I get some seemingly random value less than X. My bank can't tell me why - the best I can get out of them is some intermediate bank along the way took out some fee. It makes it a nightmare to match up an invoice with a payment.
If you wanted to exploits this effect for fun and profit you could always deduct $50 to $100 from every invoice you pay and the recipient would just assume it was some intermediate bank fee.
Switch banks? If your bank is using SWIFT, the MT103 message has fields to track this information (fields 71F and 71G) and validations to ensure the fields are populated correctly (i.e. 32A and 33B must reflect 71F and 71G correctly). Any decent bank should be able to display the originating payment instruction details for a given cross-border payment ledger entry. (I've implemented SWIFT processing fees for cross-border payments.)
Well it is a little more difficult here in Australia. I have asked a few times and the only way they can provide me with the data is to do a trace which they charge me $50 for doing. Paying $50 extra to learn that some bank took out a fee is not too helpful. I more wish I could stop it happening.
Basically, you need to find a path from your bank to the target bank account through the cheapest path of intermediary banks that factors into account fees charged along the path, expected daily transfers at that bank, the payment's impact on liquidity and interest rates of cash left on books in a particular account at a particular time of day vs. alternative options.