RPi 2B crashes, RPi 1B doesn't, running same app

[NeilAlexanderHiggins]

I am running einstein@home on a 2B and a 1B (larger memory variant). Both have been essentially dedicated to the task for months. The 2B dies every couple of weeks. The 1B chugs along without a hiccup.

Both Pis are powered from the same dual-outlet, 20W adaptor, and both are physically wired to my modem-router. Neither has a console or a keyboard - I SSH and/or VNC into both of them. The 2B has a Pi Noir plugged in and configured (tested and works), but not used.

Can I please have some hints about the diagnosis process I should follow?

[RaTTuS]

what is the voltage as measured on the test points
do the logs show anythign of interest
what does dmesg say when it is dead
are both upto date

[NeilAlexanderHiggins]

what is the voltage as measured on the test points
Checked with my multimeter and found 3.3-3.31 on the outputs of the regulators.

do the logs show anythign of interest
By "hints", I mean "hints to the uninitiated": What logs?

what does dmesg say when it is dead
As above. What is dmesg (really, I know nothing) and how do I find out what it might have said?

are both upto date
Yes

A "sticky note" (for the uninitiated) on how to approach a crashed/rebooted Pi would be a Good Thing, actually.

[RaTTuS]

loot at the 5V testpoints and measure them
cat /var/log/syslog
attach a keyboard and screen to the dead one [before and or after to see]
can you ssh into the dead one
hook up your RPi to a monitor and start playing and looking at the system
that will help much more than me making random stabs in the dark as to what may be happening.
more info is always good