I was toying with the idea of having two previously unrelated PCs having their Obligations merge, not in a "you both have the same debt now" way, but coming together as opposites.

One PC has a Favour to a crime syndicate. This syndicate is leaned on by the Empire (who the PC hates) and the crime boss "insists" the PC to come in and hunt down a mark for them. The other player has strong ties to a religious organisation, and as the crew goes about hunting the mark, they come to realise the mark is a high-ranking member of the organisation.

What do you think? Would it work? Or should PC stories be kept mostly separate?

I think the more PCs find their objectives in the same place/direction, the better.

I also prefer tying characters together in ways enjoyable to all. However, I'd caution that you should know your players well before putting them in situations that pit them against each other. The players should always understand they're playing a game and will handle the added drama with the intention you are trying to inject into the narrative. You don't want it to devolve into actual hard feelings and resentment between players.

Back in the early 90's, I've run successful games where a PC had a secret goal and killed two PC's in a fantastically conceived plan and even the players whose deaths were brought about were so "into" the game and how well everything was handled, that it remains to this day one of our favorite memories of past campaigns.

I also prefer tying characters together in ways enjoyable to all. However, I'd caution that you should know your players well before putting them in situations that pit them against each other. The players should always understand they're playing a game and will handle the added drama with the intention you are trying to inject into the narrative. You don't want it to devolve into actual hard feelings and resentment between players.

Back in the early 90's, I've run successful games where a PC had a secret goal and killed two PC's in a fantastically conceived plan and even the players whose deaths were brought about were so "into" the game and how well everything was handled, that it remains to this day one of our favorite memories of past campaigns.

That sounds very compelling indeed I know what you mean ...

I'm currently running a custom made game with three players. One is a Twi'lek Scholar, and the other two are Bounty Hunters (1 Trandoshan Gadgeteer and 1 Bothan Survivalist).

The Twi'lek Scholar is out for vengeance because her clan has been slaughtered by a vicious mining corporation after they refused to be subjugated. The Trandoshan Bounty Hunter is out to be famous and generally violent and mean. The Bothan Bounty Hunter protects the weak and is interested in bounties which are just.

The Twi'lek Scholar is doubling as the patron character. She has a credit chip set aside with a whole boatload of credits to whichever Bounty Hunter brings her the President of the mining corporation alive. The Trandoshan is interested in the job became it will bring him fame and glory. The Bothan is happy to be rid of a slaver.

This could go a lot of different ways. So far the Bounty Hunters are tentatively working together, but they have split up once or twice and attempted to find leads and get the job done in various competitive ways. The Bothan is playing it smart and buddying up to the Twi'lek, confident that if he plays his cards right he may get the money even if he doesn't complete the job. The Trandoshan is relying (I suspect) on his brute combat ability to get what he wants should things go sour.

Meanwhile there's a possibility that once the Twi'lek gets what she wants she will decide not to pay up at all.

There are a lot of possible endings to this adventure, and I can't wait to see what they do.

I prefer to let players control all aspects of their obligations, including what they are and how often they get "paid off". I "offer" suggestions, and give opportunities to allow them to be paid down...but what happens is up to the players.