The part about how much RAM. I've only been at this since pre-router days and routers and how much RAM only comes up when we are installing an alternative firmware like OpenWRT. I'm going with you are likely just confused and leave it at that.
All routers I've used in decades support transfer of 200MB files. Speed is not only dependent on the router but protocol. Windows File Explorer copies are known to be the slowest, FTP is among the fastest.

Since all routers transfer this size file, you should try FTP to compare with how you copy now.