I think some folk look at COE and want it to be WAB. Well, it's not. While historians can debate many things, records are poor at best.
Persinas are really limited, immortals not being core, the numbers of troops you must take, ie one row of long soear and three ranks of archers minimum in the standard infantry? why have a long spear if you cant have a second rank of spears. Confusion over Spara rules.
The Persians use of the spear (when used in mixed infantry-archer formations) was somewhat different than that of the Greek Phalanx, it was not used for attack, it was primarily a defensive tactic. The Spear/Shield armed front rank was primary designed to protect the rearward archers from being attached by skirmishers and light cavalry which was a common tactic in Persia. The Persians famously used the bow to decisive outcomes, albeit intermittently against the Greeks, who utilized the self-bow in a more limited way. The Persians did utilize completely spear armed units, as was the case with many levy infantry units. I think COE does a good job expressing how the units were designed and utilized historically, then transferring it into a game mechanic. In all of my research on the subject, I have yet to come across an account where a mixed archer-infantry (commonly known as Median Infantry) survived contact with the phalanx.
Another important note regarding 'The Immortals' and other 'Guard' units played a very different role in the Persian army. They were professionals who varied equipment as needed for battle. These elite units were deployed sparingly or to exploit a weakness in the enemy and Guard units were normally present if the Great King led the army.
In conclusion, both WAB and COE are different systems with similar mechanics, but different rules. I think Stuart has done a great job the Rise and Fall of Persia, but so did Jeff Jonas with Alexander the Great, but they were working with different systems/rules. Well that's just my humble opinion.