You are not alone. I'm working with level 2 support at Apple but have low hopes of a quick solution.
I have a 5 day old 2018 MacBook Pro i9 with a 2TB SSD and a 2013 MacBook Pro i7 with a 1TB SSD.
I'm using Apple's TB3 to TB2 (USB C to Thunderbolt 2) adapter and their Thunderbolt 2 to Thunderbolt 2 cable.
I put the old computer in target disk mode.
I can see the old computer's HD in Finder on the new computer.
When I open the old computer's drive in Finder, it takes a very long time for it to show the files, but they do appear (30+ seconds, possibly 60 seconds or more).
When I attempt to drag a folder from the old to the new, sometimes Finder is so slow it won't recognize the drag. I have to wait additional time before drag behavior works.
Once I drag, I get a "preparing to copy" dialog. The first time I tried it, I waited 2 hours before stopping. It seemed to be progressing in the file count, but I had no idea how far along it was and how much more it would take.
My transfer is going from a ~1000 MBps SSD to a ~3000 MBps SSD over thunderbolt. The whole 1TB drive should be able to copy in about 15 minutes.
I tried different ports. I did not try going the other direction (making the new MBP the target and copying to it).
I'm not encouraged by my Apple support conversation so far. No real answers. The suggestion is that a very long preparing to copy stage is normal, but that's not true. Either the old or new computer could index the whole drive in a few minutes, regardless of how complex it is.
Frustrating.
I've successfully used target disk mode in the past on older Apple hardware and it worked brilliantly.
In the meantime, I moved 35% of the data using an external disk. That took less than 90 minutes. And I saw none of the crazy slow preparing for copy behavior when I copied from the old machine to the external drive.
Hope we can find a solution. It should be blazingly fast.