Ok here we go...
Computer A:
An i5 Mac mini running 10.12.3 and 4 GB of RAM.
You say 4 GB isn't enough, but the memory pressure never gets outside of the green zone, so this must be crashing long before RAM becomes a factor. This one doesn't crash, it just goes unresponsive and never comes back.
Log Snippet:
http://pastebin.com/DcR0kwCtComputer B:
An i7 quad core Mac mini running 10.12.3 with 16 GB of RAM. This one crashes hard with lots of application errors on it's way out.
Log Snippet:
http://pastebin.com/5KUWYgckThat's all I have. My other computers are i5 laptops very similar to computer A. I have one older Mac Pro with 20 GB of RAM and xeon CPUs, but Bitcoin Core requires 10.8 or newer, and that old Mac can only run 10.7.
On the second one, I only see one application error, not "lots" - just a notification that the database is corrupted:
2017-03-24 17:24:14 Corruption: block checksum mismatch
2017-03-24 17:24:14 *** System error while flushing: Database corrupted
As far as the first one, I haven't tried any recent version of bitcoin on a Mac with less than 8GB and usually 16GB of RAM. I too suspect that achow101 is correct that it is a memory issue on the first machine.
Have you tried Apple Hardware Test (
https://support.apple.com/en-us/HT201257) on either machine with the extended testing to see if you do indeed have no hardware problems?