The shields stop almost everything, but run out and have resistances like armour depending on what colour they are.
Zektoid shields are good against direct stun weapons like fists but not particularly hot vs the electric damage stun rods do. In my experience, a regular Grey goes down in 1-2 successful proddings, i.e. stun sticks work fine against them. Do remember to use agents with good melee skill and zap the little bastards from the back so they can't dodge.
The theory behind shotgunning shields is that shotguns do a lot of raw damage (and shields only reduce damage by a percentage, and otherwise take it until they run out), but are heavily countered by any armour. Sectoids are too frail and naked for it to work consistently, but sometimes you get lucky.
CQC is hugging the enemy to make their shots go awry: