Both dogs and the cat are microchipped. Missy has AVID, Jack has HomeAgain, and Sassy has PetLink. Missy was chipped by the rescue, Jack was chipped by his previous owner, and Sassy was chipped by my previous vet - I had no choice in the manufacturer of the chips.
I have no idea about Jack, but both Missy and Sassy were microchipped awake, and they did just fine. Their microchips are both snugly between their shoulder blades. Jack's is migratory and at last check, was near his front leg.
I haven't had any issues with any of the three companies, besides the initial pain it was to change Jack's microchip over to me when I got him.