The big difference between LSD and Full lock is mostly the cost and the availability.

OEM used LSD's can be find easily at low cost but not always in good shape or strong enough to dispatch equally the power of your engine to your wheels.

Aftermarket LSD's are available in many size, style, quality and lock strength. Viscous, friction and geared can be found depending on car model. Remember, you got what you payed for. Cheap = cheap.

Full lock's are the most affordable options. Mini spool type are easy and its a non-permanent mod. Weld lock is the cheapest mod, it can be done by any good welder. He just need to fill between spider gear teeth, not more ( keep in mind, spatters can ruined your differential, so avoid welding projection inside the diff as much as you can ). It keep spider gears together. Generally, axles are hold only by 2 spider gears. Joining these gears together will force your two axles to turn at the same speed at any time.