Is it better to transfer all files from my old Mac to my new Mac using Migration Assistant or from an external hard drive I've used for backups of the old Mac

There are essentially 5 ways to move data from an old Mac to a new one. Though others here may disagree, I'll list them in order, from least favorite to favorite:

1. Using only Setup Assistant, as leroydouglas has mentioned, creates an account on your new Mac (which, by the way, can have the same name and password as your old Mac) and enters basic settings like time zone, your AppleID, Find My, etc. Some prefer this method as it's basically giving you a "blank slate" new Mac. You'd want to "manually" move your data and applications after this step.

The following methods all start off the same, with Setup Assistant, but then have you move everything via Migration Assistant.

1. Via WiFi. Ensure both old and new Macs are connected to the same WiFi network. This method is the least reliable, and also the slowest. Plan on multiple hours if you have a lot of data to transfer.
2. Via Ethernet cable. This method eliminates the slow transfer of WiFi, but is limited by the inherent speed limitations of the ethernet cable. Migration Assistant would be launched on the old Mac (found in Applications-->Utilities) and would be told it's transferring TO the new Mac. This is probably faster than via Time Machine backup, but would most likely require Ethernet<-->USB C adaptors, as most Macs made in recent years have eliminated the Ethernet port.
3. Via Time Machine backup external drive. This method is what I used to use 100% of the time, and it's nearly bulletproof. But, of course, the speed is limited by the type of external drive (SSD or spinning hard disk) and the type of connection (USB A, USB C, Thunderbolt). Depending on how much data you have on your old Mac, it WILL take some time...could be hours.
4. Via Thunderbolt cable. I've used this method for the last couple of transfers, and find it as bulletproof as Time Machine backup external drive, but remarkably faster. Of course, your old Mac may not have Thunderbolt ports, in which case you'd want to use the Time Machine backup. And your old Mac may only have Thunderbolt 2 ports, in which case you'd need a Thunderbolt 2<-->Thunderbolt 3/4 adaptor. I recently transferred nearly 1TB of data from my 2016 MacBook Pro to my new 2023 MacBook Air, and the entire transfer took around 25 minutes.

You mentioned you have an external drive used for backups of your old Mac. Were these backups done with Time Machine, or with a disk clone app?

Hope this helps.

MBT1949 wrote:

Is it better to transfer all files from my old Mac to my new Mac using Migration Assistant or from an external hard drive I've used for backups of the old Mac?

either way—

The most trouble free way to move to a new machine, is using the Setup Assistant on the initial boot of a brand new machine— you have one shot here. Set up your MacBook Pro - Apple Support

The second best way is use the Migration Assistant.

How to move your content to a new Mac Transfer to a new Mac with Migration Assistant - Apple Support

If you have a Time machine backup drive, and can connect it locally, the file transfers will proceed slightly more quickly, because you are not using your Wi-FI network to carry the data (in slow motion).

I prefer the Opposite of what MacMikeInOK likes. I prefer to use setup assistant at first run to bring over everything from the old backup or old Mac. Creating a new userid just seems to me to add be confusing and add clutter.

My quirk is that I like to have an Admin user that can be used JUST for Administration, and my daily-driver Userid is a different one from the initial Admin.

MBT1949 wrote:

Is it better to transfer all files from my old Mac to my new Mac using Migration Assistant or from an external hard drive I've used for backups of the old Mac?

To be clear— the Setup Assistant allows you to move your entire account to the new machine automatically with no intervention— and you pick up right where you left off...

by definition this is what makes it "trouble free."

you definitely want to use a cable connection when u̶s̶i̶n̶g̶ moving large amounts of data, if you do not have the cable to go Mac to Mac, then using a external backup drive typically has a USB, is just as effective in using Setup Assistant.

ref: USB-C to USB Adapter - Apple

USB cable connection to the local drive works perfectly well, and will be fast enough for this purpose.

USB cable is a LOCAL peripheral cable, and is not considered a good Mac-to-Mac NETWORK connection. If you attempt to connect computer-to-computer with USB, the transfer will ignore that USB cable and will revert to Wi-Fi

If the backup is up to date, i.e. no work since backing up, they're the same files.