There are (at least) two types of party splitting. One is to start with split parties which later join up and the other is starting with one party which at some stage splits, presumably to rejoin again.
I built my last game around the first sort, so that is the only experience with split parties that I've had as a developer, though I have played many games with the second sort.
A couple of issues which I think unite both approaches. The first is the inventory. I personally think it only makes sense for each party to have their own inventory. That is easy to set up when they start as separate parties, or it was for me as I used a Party Management script which allowed for that. Not so easy when the parties split partway through. How you decide to share out the inventory will depend on your story and the characters involved. For example, in one game I played, because the second party was being led by a character with good healing abilities, all the HP restoring items were left with the first party. How you share out the gear is also vital. I prefer it when you are given a chance to swap equipment around before the parties split off. I get very annoyed when the split happens without that provision, and someone in my party lacks a crucial piece of gear because I'd temporarily allocated it to someone else who is now in the other party.
The second issue is levels. How do you ensure that both parties are viable? One way to do it is to give the Reserve Party the same EXP as those in the Active Party. If you don't want to do that, you need some other mechanism in place. It is not unusual for players to have a few favorite characters which see a lot of the action and a couple that they hardly ever use.
When the parties start separate, there is a clear story-driven reason why that is so. The requirement then is to come up with a good reason why they should join together. With parties that split part way through there are again (at least) two main reasons.
The first is that you are only allowed to take X number of characters with you on this section, or maybe all sections going forward. Typically that involves some sort of hub location where you can swap your players around. I have never played a game which gave a good reason why that should be. It just seems taken as the norm that some of your party will lounge around drinking cups of tea, or whatever, while the rest go off to perform deeds of glory. I find this most unsatisfactory, and so unlikely, given that these characters are usually presented as being eager to join the quest. I suspect that this whole mechanism is a left over from the early days when it wasn't possible to swap players on the fly. I find it surprising to still encounter it. The only reason for it to continue that I can think of is if this particular mission requires such stealth that only the minimum number of characters can approach the objective without automatic detection. But that can't really be turned into a justification for everything.
The second approach is where you require two (or more) parties to accomplish something at the same time but in different places. This can be to complete some form of puzzle mechanic which e.g. two or more switches have to be activated simultaneously. This can feel a bit contrived, but is often okay because it does vary the game play a bit. Then there are the cases where there is a coherent story-driven reason why a second party needs to go off to do something while the other party gets on with another aspect. If it is just done because well, why not? then it usually comes across as lame.
Executive summary coming up - as a mechanism it can add interest and strategic choices, but as always it comes down to implementation. I personally think it needs to be story-driven.