I can't upgrade migrate to new Mac

Update, upgrade and migrate are three different things.

I assume that you mean to MIGRATE your stuff from the old mac to the new one.

WARNING: you should ONLY migrate the users; do not try to migrate applications, "settings" or "other files"

To migrate directly from one mac to another, you have to initiate Migration Assistant on the old mac.

Did you?

So:

1) on the old mac, launch Migration Assistant, and choose "to another mac"

2) on the new mac, choose (I think you already did) "from another mac, disk or Time Machine backup"

then select ONLY the users

3) Let it do its thing

ALSO: the above should work, provided that the two macs are on the same Wifi network; usually it is better and quicker to just have a Time Machine backup of the old mac, attach the backup drive to the new mac, and use that for migrating.

Q - " The software update pane is just whirring and whirring and I don't think it's going to upgrade. What can I do? "

A - Addressing Only that aspect refer to bellow>>

There are factors:

1 - Like poor Wifi connection

2 - Slow wifi connection

3 - Too many other people downloading at the same time and Apple Severs are overloaded

4 - Software on the computer interfering with the download process including AntiVirus Software

Notation: Disabling the AV Software may or may not solve the issue. Removal of the AV Software may increase the chances of the download to perform as expected.

5 - Running behind a VPN which may increase Packet losses or corruption of the download 

6 - If via wifi too many Other devices using the wifi at the same time reducing the Bandwidth to your computer. 

7 - Best Results are via Ethernet Cable to Router