Only if the files are tens of GB each. And even then you have Windows file system overheads to tend to. Via file explorer you will not be transferring at up to 7000MB/s for example (typical good speeds for higher quality gen 4 drives). Between gen 3 and 4 it's essentially going to be the same performance for large file transfers inside Windows unless you use tools that bypass the Windows Explorer transfer methods (FreeFileSync etc). And even then the difference is in single digit seconds between say a 15GB bluray movie rip.
That's also all assuming both drives are gen 4, because if the source is gen 3, and the destination gen 4, then you're only going to be writing at gen 3 speeds as that's the fastest the read can happen.
Bottom line? Makes no difference. Just get the best spec drive for your budget.