Transfer files from MacBook Pro with USB-2 ports to new MacBook Pro with USB-3

Could you be more specific about what machines? This gives a lowdown on the various connections that might work:

How to move your content to a new Mac - Apple Support

How to use target disk mode to move files to another computer - Apple Support

I don't believe you can set up your old MBP in Target Disk Mode with USB. You could remove the drive, put it in an enclosure, and then connect that to your new one. That's a lot of work though. Maybe FireWire or Thunderbolt 2 (if you have it) via an adapter.

You might also be able to use ethernet from the older MBP to the newer USB-C port with an ethernet adapter/hub/etc. The article recommends using Wi-Fi.

if you can get both computers onto the Internet without re-cabling, there is already a pathway between them (through the Switch function of your Router).

You can turn on File Sharing and use File Sharing to transfer your files.

How to connect with File Sharing on your Mac - Apple Support

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If they’re both on computers, data can’t be transferred that way.

If one of them is on an external drive, an USB(not USB-C) cable.

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