Is it still possible to remove the hard disk from the MacBook?
If so, put that disk in an USB 3.0 hard disk cradle (or lightning/thunderbolt/however these hardware ports are called on Mac nowadays) and transfer the files to the new system/hard disk. That eliminates one copy step from the external disk scenario (old computer -> external disk -> new computer).
Better yet, if the new Mac system has the capacity to support 2 or more hard disks at the same time, take the hard disk from the old system and install it for the time being in the new system. Now the internal hard disk controller of the new system can pump the data from the old hard disk to the new hard disk. That is the fastest way to transfer a boatload of data to a new system. When finished, you can put the old hard disk back into the old system and all will be well again. On both systems.
Are you transferring between two Mac computers or do you also change from one OS to another?
If so, there are drivers for the new OS that enable read-only access to the file system that Mac uses. Those drivers enable you to access the content safely. You still need to take the old HD out of the Mac and put it into a hard disk cradle or directly into the new computer.
But what to do when it isn't possible to remove the hard disk from the old system? Then the external hard disk scenario is the simplest and likely the fastest one. transferring boatloads of files through WiFi is always slower and more prone to errors than through a wired connection between computers.
For example: in my own setup I have 2 Windows computers, each has a 1GBit/sec network card and both are connected to a 16 port switch, each port capable of the same 1GBit/sec speeds. A very standard or common setup. Transferring files from one system to another goes with a speed of about 70 to 80 MByte/sec continuously. On average. That should give you a way to calculate how long the transfer could take with a wired connection between systems, given the specified amount of data.
You can expect similar speeds or even a bit faster when both hard disks are connected directly into the same computer. Expect half those speeds when using a cradle. Connecting both systems using WiFi and you will be happy when transfer speeds reach cradle speeds, depending on connection quality.
Remember: WiFi is made for comfort, not speed. No matter what salespeople say, WiFi is made for comfort, not speed. Enterprise level WiFi equipment might get you to (somewhat) higher speeds, but that kind of equipment comes at cost and will always be capped by the max capacity of the WiFi hardware inside the old and new system.
An external hard disk is really much simpler in setting up and still remain reasonably fast at very acceptable cost.
External hard disks that use 2.5inch spinning disks do not require a separate power supply, but sacrifice speed as a result. There are also external hard disks that do require an extra power supply and these usually contain a 3.5inch hard disk inside, which are noticeably faster. You are still capped by the maximum capacity of the hardware port you are using to connect the external hard disk to the computers.