I did find one relevant difference. PADCTL_EQOS_EQOS_TXC_0 is set to 0x00002050 for JP 5.1, while it is 0x00002400 for JP 5.0.1. Reading the TRM, 0x2400 makes more sense.
As soon as I manually set it to 0x00002400, the Ethernet starts working!
busybox devmem 0x02445058 w 0x00002400
I found that the invalid configuration of a completely different module (USB) caused the GPIO controller to grab pin E.00. I was not aware of the priorities of the gpio controller vs. pinmux. Good to know.
Fixing that pin also solved the Ethernet issue. :-)
Thank you