1. FPS set in the (real) Shadowrun world.
The world of Shadowrun is, IMO, more important than the rule-set. A single player FPS set in the world of shadowrun, telling an authentic shadowrun story could be a very good game. This is probably the weakest of the options,
Agreed. Shadowrun has an INCREDIBLY rich story and this option is, to me, taking the Microsoft option of ignoring all that and just making a generic FPS with fantasy races and calling it a win. At the end of the day, the elements Shadowrun has to work with to construct an FPS make it a very bland FPS. You would also create a balancing NIGHTMARE with magic and if you tried to integrate things like hacking and Technomancers, it would be a ginormous trainwreck.
1a. Rainbow Six (original) version of Shadowrun.
More of a variant of the FPS shooter style game, but while the FPS one focuses on telling a story (ala Halo) this one would focus more on the tactical planning side of doing runs. It would still be FPS, but would include a larger focus on planning out the runs over simply running and gunning.
Again, I think you'd run into the same problem as the first option. It would be better for longer, but eventually it would get stale and feel more like the gameplay was just a side-note, a way to drive the cut-scene story along.
2. Grand Theft Auto style Shadowrun
Probably the closest non-RPG style game we could get to a shadowrun game. The over-all set up of GTA would work for Shadowrun. Open world Sandbox, shady locations, people giving you missions, etc. Someone with good modding experience could probably put in a lot of work and mod up GTA 4 to be a shadowrun game. For this you can think of what would be a natural blending of the old Sega game with modern sandbox gaming.
This isn't a bad idea but I think this lends itself more to the violation of what you actually are in Shadowrun; you're a criminal who shoots people in the face for money. GTA puts you more on the level (in actuality, not in depiction) of a super-hero who can square off with massive squadrons of cops and walk away. I think it would end up being more like City of Heroes than GTA and the system of punishment you'd have to institute to keep people on a more "Shadowrun" path would have to be so draconian and brutal you'd ruin the game.
3. Metal Gear style of Shadowrun
Another Action game version of shadowrun, this time the idea would be to use a set up similar to the "tactical stealth action" of the MGS series in a shadowrun world. The entire game may take place during a specific run.
See #1
4. "Mass Effect" Shadowrun
Here we start touching in on the Shadowrun world from an RPG stand point. Still rather action oriented, because I think shadowrun warants it. The system can be tweaked to fit all the different playstyles.
Probably the most realistic incarnation of a good Shadowrun game. It would be a daunting task though because Shadowrun is such a massive game world. You'd have to compartmentalize it somewhat, though it would give you room for sequels and add-ons.
5. Shadowrun MMO
The holy grail of shadowrunning. An MMO sandboxy world with everyone playing shadowrunners of different ilk. The ability to hire on fellow runners to complete a mission, deal with the mega corps, etc.
As much as this gets passed around as an awesome idea...I dont think it would be so amazing. The biggest issue would be balance; how do you balance out the different aspects of the game and still have classes and races that arent basically a carbon-copy exercise in enforced mediocrity? That alone would be a monumental task. You'd need a company DEDICATED to the game that knew it well to sustain it and have it work out well. The fanbase is incredibly critical and vocal but dedicated. The MMO market is already well-saturated and difficult to break into.
I think option 4 is the most realistic chance for a good Shadowrun game.