Hey Adam,
Ok, Security boxs where just a unique Klingon system feature in SFB. Only Klingon ships had them and they were to provide extra support to your marines (enhanced security) and where able to help withstand direct assults to the ship (can't remember if they helped defend against Hit & Run attacks aswell). Ever noticed in SFC: OP that when you try to board a Klingon ship, you virtually need a commando ship to take it over (or literly cripple the vessel in order to have a chance to take her over)? Security stations in SFB where created by the Klingons to help guard the ship against a mutiny and had the added benifit of help defend the ship against boarding. Klingon ships were succetable to mutiny because a portion of their crew was slaves/Prisoners from other worlds. Only Klingons had to worry about Mutiny. SFC though, does not take into account of mutiny so they are just added extra defense against boarding and additional hit points.
Bridge boxes are kind of funny. You only need one box (1) to run a ship, but usually the larger the ship, the more bridge boxes it will have. Their is no real added benefit to the extra Bridge boxes other then extra hit points to the Bridge system. Would have been interesting if ADB had made it where the more bridge hit you take, the less effective your system become... much like how sensor and scanner damage WILL effect how well your direct fire weapons react.
Lab boxes are their for the benefit of science and scanning for the ship. Ever noticed that most feds have much more labs on their vessels then most races? Feds have the advantage here. In SFB, they helped give better sensor data to your ship for long range scans and more percise scans. I'm not sure if these advantages are reflected in SFC. I do know that the "long range scanner" button does seem to give the feds a slight edge over other races in the amount of distance so it may indicate the extra Lab boxes at work (this feature was in SFB aswell). For combat purposes though, they are little more then extra hit points for the vessel. If you haven't noticed, many Fed ships in OP that are refited in the late and advanced era have extra "AWR" (Auxilary Warp Reactors). During the General War, the Feds ripped out some of the lab boxes in place of AWR's for extra power to the ship. This helped a lot for their warp power hungry photons.
Tractors Boxes are just that... they are the number of tractors available on the ship. You can use tractors of course to tractor other ships or incoming missiles. More tractors you have, the more targets you can tractor. But since Tractors require energy to use them (like most systems) you need the available power to do that. You can of course pump a lot of power into one tractor to handle one target (like a ship trying to do negative tractoring) or you can set all your tractors to do multiple targets. If you didn't know, you can press the "C" key on your keyboard to automatically tractor any incoming missiles (or fighters, can't remember if SFC does this) by the amount of Tractors you have. Its a very handy feature in SFC for missile defense incase you don't want to use your phasers to eat up incoming missiles or just plain don't have any charged weapons to use on the incoming missiles.
Mech Tractor Boxes are suppose to be special tractors used to tractor your races PF's (Fast Patrol Boats). If you don't know what PF's are, they are basically a miniture ship (with Miniture ship systems) in a tiny hull. They are larger then shuttles and fighters, but are smaller then even Corvettes/Police ships. The closest thing I can think of that might resemble what a PF might be would be Star Treks "Runabout" class seen frequently on DS9. Not quite the same because at thie time period they don't have minimal lifesupport systems (crew where space suits during missions), but similar. In SFB, PF's where capable of warp speed (unlike Fighters and shuttles), but where so limited in Range, they had to be carried into battle by their large mother ship... the PF Tender. The Mech Tractors are pretty much a Tractor Beam with special assemblies on it to house, refuel, repair (to some extent) your PF's. In SFC, these abilities are somewhat represented, but not exactly to SFB doctrine.
Transporter Boxes are just how many Transporter pads you have installed on your ship. The more transporters you have, the more boarding parties or things you can transport in one turn. If you haven't noticed, Klingon and Gorn ships have an advantage here. They have lots of Transporters and Gorn especially have and edge in ground combat so watch out!
Well, I hope this info is useful to you on SFC OP.