Not necessarily better but the question is, what is appropriate for your requirements.
The 5600 is the largest selling control valve made. It is an older 3/4" design which has its limitations but if your requirements are within its capabilities, then it should work well for you.
The 5800 series is the newest series available, with additional features as well as models which offer up to 1.5" connections and higher backwash capabilities to support larger diameter tanks.
Fleck, similar to Clack, no longer offers their newest valves to the DIY & online market which is why 5600 series valves are typically found online whereas 5800, 5810, 5812 are not.
A quality fibreglass tank such as Structural, Clack, Enpress etc is commonly used with a gravel underbed. Most softeners use this configuration as it is low tech and reliable.
Vortec tanks had some issues early on but the smaller diameter tanks seem to be more reliable now and so are being recommended with little hesitation.
If you state your water conditions as well as your household water requirements (gallons per month or number of residents), your main service line diameter, fixtures with high flow requirements (ie; multi-head showers, soaker tubs etc), as well as the size of softener you are considering, we can then provide recommendations for efficient salt use or other benefits.
