Basically salt softners have media which have sodium ions on the surface. When the hard water with calcium flows over the media, the media lets go of the sodium and attracts the calcium. When the media gets "full" from the calcium (usually determined from your hardness and anticipated water usage) the back wash occurs which basically reattaches the sodium back onto the media, letting the calcium go out the backwash - with the extra sodium in the solution.
The back wash is based upon the hardness in your water - say 15 grains per gallon (1 grain per gallone is ~17 ppm calcium ions) for instance and an assumed amount of water you would use during a day - say 1000 gallons. So in a given day, with these numbers, the softener would remove 15,000 grains of hardness The softener media has a certain capacity of being able to remove the hardness - say 300,000 grains. So in this example the softener would backwash about every 20 days.
When I design softeners for commercial applications, I typically size them to backwash at most once per day. When I had one in my home, it backwashed about once per week.
I read the website about the salt free (Pelican) and I am not sure if it is based on sound science, but it appears that it converts the hardness molecules (calcium carbonate) through some type of friction across the media to a form/shape that will not adhere to the sides of your pipe. It sounds similar to the magnetic types of water softeners that use magnetism to keep the hardness molecules from forming scale. Again, I don't totally understand the "science" behind it to have a real opinion.
The magnetic type of water softener has a lot of anectdotal evidence but no scientific backing - no testing, no support. I don't know if the salt free has any scientific backing, but it must have anectdotal evidence for people to still be selling them.
From the website, the salt free system does not require flushing.
I wouldn't let the backwash of a salt system go to a septic tank. I did some research a few years ago when I was on a septic system, and while the data was somewhat inconclusive, the side that said it was ok to send the backwash to a septic system was funded by the water softener industry - so I am not sure it was unbiased.
I wouldn't think there would be a problem with sending the backwash to the sanitary sewer since you are typically charged on what water you bring in - not necessarily what you send out.
See if you can find one that is relatively cheap and see if it works. Soft water definitely feels/acts different in the shower and sink. If it doesnt work you can take it out and try the other type.