TL;DR - SWG is far cheaper PPM/$ for most users than Liquid Chlorine. Upfront costs are higher, and your payback period may be a couple years or more, but your PPM/$ cost WILL be lower.
I was on the fence too before I crunched the numbers (and had them crunched by
@Newdude a few times !!)
First - there is a difference between 'Cheaper than Chlorine' and 'Payback Period'.
SWG Chlorine is without doubt cheaper than 'in-the-jug, buy it once a week LC'.
Example :
1 gallon of the cheapest LC around adds 5ppm to my pool.
Cheapest LC locally is from Menards at effectively $3.99+tax/gal
That essentially works out to be 5ppm per $4.23 = 1.2ppm per $1 spent.
My RJ-60+ cost me $1499.
The cell ($800) is rated for 15000 hours, generating 3.1lbs of Chlorine per 24hours - so that works out at 15ppm/24 hours, or roughly 9375ppm (in my 25000 gallon pool). I've validated this rate based on the % setting on the SWG, and the PPM measurements in the pool - its pretty much bang on.
For arguments sake, lets assume the cell only lasts 66% of it's expected lifecycle, and call it 5500ppm lifetime.
5500ppm / $800 = 6.9ppm per $1 spent.
So assuming the best case for Liquid Chlorine, and the worst case for my SWG, it still costs me one-sixth as much to use the SWG versus the jugs.
Plus, I'm not factoring in the LC being little more than $4.23, in that you have to fill out a rebate, plus gas to go get it, time, storage, stamps, recycling the empty jugs.
Plus, if you use the full expected lifecycle, the number is closer to 12ppm/$1
Payback time is different - the total cost of my SWG was $1500 (I installed myself) - I would have to not buy LC for about 3 years to 'pay that back' - assuming LC stays the same price it is today, and I make no allowance for any of the hassle factors. However, once it's paid back, I'm saving $400+ a year, based on TODAYS LC prices. Who knows where they'll be in 3 years time.