In any litigation, including divorce cases, one of the first decisions that must be made is where to file the case. Even when both parties reside in the same state, different courts might have the legal authority to hear the case - which one is appropriate in your case?
This is called venue and usually it's a pretty clear matter. For instance, in Arkansas, venue clearly lies in the county where the spouse who files for divorce resides (or the first spouse to file, in the case of competing filings). See the Parker v. Parker case for a fuller discussion of this rule.
What difference does it make? While any Arkansas court (or any state family court) should apply the same rules and laws as in any other family court in the state, where venue lies can absolutely affect the way the litigation is conducted.
There's the obvious hardship that arises when a party is forced to litigate a case in a court located in a county on the other side of the state. Court appearances can then become quite costly, requiring out of pocket expenditures for travel for both the party and the party's counsel, potentially.