In most cases, phalanx is ever so slightly better than a wedge for a attacking.
The type of phalanx/wedge shows the placement of the troops on the battlefield. So, in Infantry phalanx (the default and only one not behind research), Infantry are in the front, Cavalry behind them, and ranged in the back. LM combat mechanics are very straightforward. The troops "lock on" to the closest target. Once that "target" (i.e. all of one type of troop) is killed, the troops then find the next closest and fight that. So if you are fighting against a level 16 castle (which has to be Infantry Phalanx because the other two require Academy 17), you know the infantry will be in front. That means you go to cavalry phalanx, so that your cavalry are in front. Thus, your cavalry fight their infantry. However, keep in mind that their ranged will lock on to your cavalry, since your cavalry are the closest target. So sending 100% cavalry against 50/50 Infantry/Ranged is not the wisest.