I've tested both official APNs. I see no difference in latency, speed-test throughput, nor any change in blocking behaviour. I've not studied the routing used.
The only difference I've noticed is many more dropped pings using three.co.uk. I've not noticed any problems with packet-loss in normal use, so I guess this is an ICMP deprioritising setting somewhere.
Three unlimited SIMO, replacing 3 km ADSL line.
Previously: BT ISDN, Nildram, Plusnet, 186k, EFH, Be*, Plusnet (again), Pulse8, Sky, Plusnet Business, TalkTalk Retail.