First off, double check that you had the 5V connected up correctly, and the 5V is actually still 5V, as something on the powersupply side is the most likely thing to damage both boards.
There's no point looking at other issues, untill you are 100% confident that you have covered the basics (we all make stupid mistakes!)
Second, are the VFD connections in the diagram, the only connections you've made to the VFD (excluding the main power in/earth), and you've not connected the CN (Common) terminal to gnd at any point?
If you were to connect the Common terminal of most VFDs to ground, you can do a lot of damage, as most drives float this around mains voltage, so it would most likely damage something as soon as power was switched on. If you had done this, and you're power supply is protected by an RCD, the RCD should of tripped.
Other than those issues, I can't see anything else that could damage both boards. The C41 outputs are all opto-isolated (or at least they should be..) so any wiring issues on the output side should limit damage to that board, and any issues with the ESS wiring side is most likely to just damage the ESS itself, as I'd doubt enough current would get back through the ESS circuitry to put any major spike onto the 5V supply to damage the other board.
One other possiblity is something conductive i.e. a bit swarf/filing/stray screw/nut/washer has got on somewhere and shorted something it shouldn't off, but then that shouldn't of killed both boards, unless it caused an issue with the 5V supply.