There is a need to bring some clarity here, there is opinion and there is fact.
They are all salt pools, when sodium hypochlorite (Chlorine) breaks down it leaves behind salt in the water so over a period of time the salt concentration rises and can equal a mild salt concentration similar to that used by a salt conversion proccess, which uses an electric cell to break salt water down into chlorine so that stuffs that argument!
The active chlorine level (hypochlorus acid) in a pool is quite low as chlorine stabiliser cyanuric acid (CYA) bonds chemically to the chlorine to protect it from the suns UV rays which other wise would break down chlorine in just a few hours. This means the active chlorine level could be lower than that supplied by municiple tap water which most people bath in without issue.
What tends to be the issue is the high levels of chlorine experienced in municiple communal swimming pools which is far higher than required in a domestic situation and as is the case with most municiple indoor pools which don't contain CYA stabiliser so the active hypochlorous acid level could be 10x the amount used in a domestic situation.
What difference does that make?
Chlorine will attack anything it will kill bacteria and algae and oxidise and anything else it comes into contact with from hair to skin cells and body oils, sweat etc. That leads to what are known as disinfection byproducts (DBP's) almost all problems related to breathing and skin irritation are actually related to the DBP's and not to the chlorine.
DBP's will occur in both directly chlorine dosed pools and salt water converted chlorine pools and that is down to the correct management of the pool and accurate testing. Because of the lower level of active chlorine in a domestic pool compared to a commercial pool there are correspondingly lower levels of DBP's so it is rare even for eczema sufferers to have a problem in a well managed domestic pool. That doesn't mean it doesn't happen but its rare as clinical chlorine allergy is very rare.
There is some anecdotal suggestion that the splitting of salt water in the cell releases not only the chlorine gas but an active form of oxygen and oxy radicals which also help oxidising bather waste etc, it certainly used to appear in some advertisers information (Ecosmarte etc) but in reality the level would be so tiny and the split molecules of water will re combine very quickly (within 0.5 sec) which at pool flow rates (1.7-2 metres/sec) would mean they never reach the pool so don't really count for anything.
With salt water chlorination you are just generating a tiny amount of chlorine on site rather than transporting it from a shop, however as mentioned above the cells process also produces bubbles of oxygen and hydrogen and these bubbles will tend to cause a continual drift upwards in the pH of the water compaired to a similar dose of directly injectected chlorine. Both forms of chlorine cause a pH drift but it's more noticable with a salt generated version so a pH regulation via a dosing pump should be incorporated.
pH regulation is by the addition of acid of some type, often hydrochloric. That also stuffs the salt chlorinators advertising blurb as they often say "Natural with No Harsh Chemicals" somewhere and that is just rubbish as hydrochloric acid as most peopl know is quite harsh, that said the levels are very dilute so not a worry but advertisers wouldn't let that get in the way of a sale! Both types of pool are a chemical soup and that's the real fact.
It would be quite wrong to propose any suggestion of the "best pool" for your situation without a site inspection. If you are on clay which moves then a proper site inspection will need to take place.
These days fibre glass pools are actually quite rare, far more likely to be a polyester resin as the old glass fibre had issues with osmossis blistering and frequently eneded up requiring a liner. They can "float" out of the ground if the water table gets high or the ground saturated, hence the name "Boat pool". A hydrostatic drain valve can help in some situations. Even concrete pools have been known to float up despite the weight so a site survey and not a forum opinion is the route to take.
If movement is an issue there are polpropelene panel kits and liner combo's which can facilitate movement without damage so there are all possibities.
Don't overlook insulation from your pool design, In the UK all new outdoor pools have to be insulated (Part L of the building regs) because it works. In France however the pool industry is pretty much stuck in time (around about the late 50's early 60's in technology so most pool companies don't have a clue) It may seem silly to some but having your water a few degrees warmer at the ends of the season without resorting to heating would be a godsend and if you are heating it could result in needing a heater with half the output and therefor half the electricity bill. I know enough owners who didn't want to waste money insulating their pools as they weren't going to heat them, only to say something completely different a couple of years on especially as they get older and it's more expensive to do later.
Whilst on the subject of electricity, French built pools are not energy efficient! some are not even efficient, The big 3 pool companies build appalling examples of the flow systems and the water is important, the better kept the water is the less chemical of any kind it will use. Companies with the letters D, W and M at the start of their names should be avoided, they employ sharp suited sales forces and their product are amongst some of the worst pool flow systems I have ever witnessed, yes they have built many 1000's of pools but I should be grateful as it produces work for people like me to go round putting things right but better to have built the thing well in the first place.
What do I mean by the above?
Water has to be pushed around the pool in an efficient way to circulate chemicals and filter out dirt etc. Anything that interferes with that cost you money over the years. There are a rising number of pool companies using mono block filtration systems, the big 3 as mentioned above + numerous others.
What's wrong with them?
These systems are quick and easy for the builders to install and that produces a better bottom line profit for the builder of the pool. For the life of the pool it will be costing you more money though. This is because mono block filtration uses bags or pleated filters etc in front of the pool pump. It is not efficient to suck water compared to pushing water. Water behaves like air, try sucking out the candles on a birthday cake compared to blowing out the candles and you will get what I mean. Highly efficient, state of the art flow design can run your pool on 85%-90% less electricity than a standard pool or mono block filtration system with higher water quality as a result and that allows lower chemical usage which of course means less irritation for everyone including eczema and asthma sufferers.