And bitcoin wallets are NOT that resources intensive.
Bitcoin Core is because it is also a full node. Verifying and relaying every single transaction and block is quite resource intensive.
I do photoshop work that uses tons of memory and maxes out most of my CPU. Bitcoin is a lightweight compared to that.
But to answer your question, one of the computers has 16 GB of RAM, the other has 4 GB.
One is a dual core i5, the other is a quad core i7.
Both are 2012 Mac minis with intel HD 4000 graphics.
I don't have any kind of active firewall, just a standard router.
Are both of your computers crashing? Bitcoin Core will crash with the 4 GB RAM one as 4 GB is no longer enough memory to keep a node running. It will run into an OOM error and crash.
Core shouldn't be crashing on the 16 GB RAM one unless there is some other issue at hand.