AUTO:
Pros - plant matures by age, you can keep lights on 18/6 until harvest, you don't need as much space per plant, depending on strain you harvest around 8-10weeks after sprouting the seed, you can go perpetual in the same grow room, simpler on nutes and medium, there's some really good auto strains.
Cons- you can't grow 5ft monsters, you can't keep strains unless you seed them, cloning and re vegging are a no-no, yield (unless you have a small space)
PHOTO:
Pros - You pick the age you want to flower a plant, you can grow bigger to gain a bigger yield, cloning, mothers, can keep a strain perpetual, you can keep a plant vegging if something happens, more strains to pick from, easier to breed
Cons - more space for bigger plants, for perpetual you need 2 grow areas, you use more nutes per plant the longer you keep them, from seed takes longer to harvest when vegged
That's just off the top my head. neither of them really have cons, each grow area requires its unique pros and cons. Those are just my opinions coming from my grow room.
Its mostly down to what strain you want, (not all strains are autos and not all auto strains you can get),
your grow area, (work out what you have and how you can use it well),
and your opinion.