The console will show the NSLog() output from an app running in the simulator. The crash logs are saved to file.

I have found some in my home directory under

~/Library/Logs/DiagnosticReports/

They have a file extension of .crash

Something I haven’t yet figured out is how to get them to generate even if the debugger grabs the EXC_BAD_ACCESS signal.

Update

Currently, (OSX 10.11.6), the .crash logs in ~/Library/Logs/DiagnosticReports, are when the emulator itself crashes. Logs for an app crashing (but the emulator device is still running fine), are in:

~/Library/Logs/CoreSimulator

Per crash, there is a sub-folder with a unique id. Sort by date, so that your recent crash is the first sub-folder. Inside that, start by looking at stderr.log and system.log.

Also directly under CoreSimulator, see CoreSimulator.log and Simulator.log.