The first point of comparison between the two, according to Antipholus of Syracuse, the twin brothers are lost to each other, with one residing in Syracuse and the other in Epesus. In fact, Antipholus of Syracuse (Ant. S.) is on an intentional quest to find his lost brother, Antipholus of Ephesus (Ant. of E.):
Ant. S. I to the world am like a drop of water,
That in the ocean seeks another drop;
Who, falling there to find his fellow forth,
Unseen, inquisitive, confounds himself:
So I, to find a mother and a brother,
In quest of them, unhappy, lose myself.
Conversely, while Ant. S. seeks to restore the bliss of his domestic circumstances, Ant. E. is embroiled in the sabotage of domestic any hope of domestic bliss; in this they are very different:
Ant. E. And buy a rope’s end: that will I bestow
Among my wife and her confederates,
For locking me out of my doors by day.—
Another difference is that while Ant. s. claims Christian principles behind his (justifiable, to his eyes) threats of violence, Ant. E. simply plots out wicked deeds without hinderance of Christian scruples:
Ant. E. [To Ang.] Get you home,
And fetch the chain; ...
... to the Porpentine;
... that chain will I bestow—
Be it for nothing but to spite my wife—
Upon mine hostess there: good sir, make haste.
The most notable early difference between thsm is that Ant. S., the one with christian scruples who is searching for his mother and brother, has wealth, "The gold I gave to Dromio is laid up / Safe at the Centaur; ..." while Ant. E. has less:
Dromio of Ephesus (servant of Ant. E.). O,—sixpence, that I had o’ Wednesday last
The saddler had it, sir; I kept it not.
In sum, one is a moral man with Christian scruples who is saddened by the loss of mother and brother and is in quest of them, whereas the other is a quarrelsome man who is in quest of pranks and tricks and drink, though a respected merchant of Ephesus. They are introduced as antithetical--opposites--of each other.