I've both run and played in games like this; they are, to me, the best kind.
As mentioned above, the biggest headache is in-game time management, so the two (or more) parties don't get too far adrift. Some sort of enforced downtime (training, rest, item manufacture, whatever) between adventures is Your Friend here, as you can simply vary the downtime for each group to suit what you need. Occasionally, if you're building to some big in-game event and one group gets there early, you might have to sink a session or two for that group (or let them play a sub-party) so the other can catch up.
One *key* ingredient, also sort-of touched on above, is to give characters in both parties good reason to know each other. Simplest way to achieve this is to start with just one big party, then split it in two after the first adventure. Allow and encourage players to switch games between adventures where it makes sense (though I ran aground on this once: I had two parties each working on different angles of the same plotline, and had very carefully set things up over a number of adventures such that one group knew what to do but not why, while the other knew why things needed doing but not what...until two of the players decided to trade games halfway through...)
If the characters know each other, some of your time-management might take care of itself; one party might decide on its own to wait for the other: "Hey. We're down a Cleric because he died in our last adventure; but last we saw the Southern party had an extra one, so let's wait for them to get back to town and realign ourselves..."
A common base of operations (castle, farm, whatever) also helps here.
What you'll end up with, if you're lucky, is a set-up where parties form and merge and split on a rather fluid basis throughout the campaign. And these type of campaigns are best run long...very long, if you can manage it. Minimum 5 years.
Lanefan