Bleach and 12.5% sodium hypochlorite liquid are the same thing, only different concentrations. Both are liquid chlorine.

Let's keep it simple: Up until a couple of years ago "Ultra Bleach" was 6%. I buy 12.5% LC for about $19/5 gallon carboy. I paid the deposit on my 3 carboys years ago and just keep trading them for new ones when they are empty--don't have to pay the deposit again. Be that as it may....at $19 for 5 gallons of 12% (really 12.5%, but we are keeping it simple) that's an equivalent cost of $1.90/gallon of 6%. So, the answer for that is obvious: If a gallon of 6% is more than $1.90, the 5 gallons are cheaper. If it's less, then the bleach is cheaper.

Actually comparing 8.25%, which is sold in 121 ounce bottles at my local ShopRite for $4.19 or $.03/ounce is quite a bit more because the same liquid chlorine at $19/5 gallons is $.0296/ounce...but the 12.5% is half again as strong.

Therefore at $4.19 a jug of 8.25%, vs the 5 gallon 12.5%, it costs 50% more for the same amount of Free Chlorine in your pool. If you add in the deposit, it comes to $.045 for the 12.5%--about the same price...but everytime you replace the 5 gallon jug, you cut the $10 down. After 10 jugs, it's only a dollar extra--and $.03125/ounce...much cheaper than the bleach.