I have used all three over the past thirty five years.. I have done about everything that can be done (wrong) while by making poorly assumed "educated guesses"....I have found nothing that compares to alum as a surface water coagulant but alum has at least two shortcomings.-1.It forms three separate concurent hydroxides that shift in concentration,and solubility, dependent upon pH... The most cationic is at the lower ph.The least soluble and the most cationic concentrated form is at pH 5.7.....These variables are reasons that alum has been identified as the culprit behind fouled heat exchangers..Since the pH falls by increasing concentrations and the optium pH may easily be passed with increased demand,, Many times sodium aluminate is added in conjunction with aluminum sulfate (or chloride) to keep the pH at a given "fixed" level. 2.Alum dewaters poorly in comparison to ferric BUT for any given amount of cation demand (chemical usage),-The ferric ion Fe+3depresses the pH far greater than an equavelent alum ion Al+3 requirement- assuming that all FMA (free mineral acid has been removed from both samples).......You can prove it by titrating a given quantity of ferric ion and the same quantity of aluminum ion against a standardized caustic solution to pH 7.0......Also, ferric chloride is much more soluble than ferric sulfate (copperous) but it is extremely corrosive, even on stainless steel at levels approaching 1500ppm...Also, it is very expensive to form ferric hydroxide with caustic soda and it is also a much less effective flocculant than ferric and lime from a number of standpoints....BUT ....FERRIC CAN LOWER HARDNESS in surface water clarification whereas alum will not..Good luck!