I will answer in form of small "glossary":
MOSFET (shot for Metal Oxide Semiconductor Field Effect Transistor) - act as a electronic valve,its resistance (how "open" is) can be controlled with voltage on gate
FET - more general term, there are other types of FETs other than MOSFET, but for drivers MOSFET is only used,so FET is just short term for MOSFET
FET driver - driver that uses FET as control valve, on BLF "FET driver" means DD (Direct Drive) FET driver, which is simple type of driver that uses FET either in fully opened or fully closed state; medium and low modes are accomplished by using PWM (pulse width modulation). In short, good sides are low cost and low generated heat in FET (but that depends a lot on FET and max. current); bad sides are driver doesn't actually regulate anything,it's just like open or closed mechanical switch,so current is not regulated,and low Vf emitters can be fried,LED operates at usually significantly lower efficiency on lower modes,lower modes are not regulated too so brightness depends a lot on battery,resistances etc.
Linear driver - for ex. 7135 IC,LD-A4/B4 also uses FET as control valve, but in a way that valve can be anywhere between "opened" and "closed" state, not just fully opened or closed. Driver adjusts control signal (which controls valve resistance) so that output current remains constant and independent on LED,battery voltage,resistances,temperature etc. Linear drivers can use also PWM to get lower currents (like with 7135), but also can be controlled without any PWM (like LD-A4/B4). Because LEDs have significantly better efficiency(lm/W) at lower currents, driving LEDs with lower constant current is better than driving it with pulses of high current.
For example, any LED will be much more efficient if you drive it with constant 100mA , and not with 2% PWM pulses of 5A (which DD FET drivers do).
That's why there are drivers that use one or more 7135 chips in combination with DD FET to get better efficiency on lower modes. 7135 are still PWMed to get any modes in between 350mA steps.
LD-A4/B4 is linear driver that doesn't use PWM so on any mode current is "real" - no pulses,just a DC current,and LED runs on max. theoretical efficiency. That's equivalent to DD FET with almost infinite number of discrete constant current chips like 7135.
So good sides of linear(non-PWM) drivers are true current regulation (equals to constant brightness and you don't have to worry if LED would survive) and maximized LED efficiency on lower modes; bad sides are increased complexity and heat that's generated in MOSFET. In DD FET driver that heat is "transferred" to LED which causes lower efficiency of LED, so in linear drivers FET acts as sacrificial component that dissipates extra energy from battery.
Problem with heat dissipation in MOSFET is not problem by definition,it is only problematic because FET on linear drivers are on FR4 boards and have relatively poor thermal connection to heatsink (flashlight body). In that case max. power dissipation in MOSFET can be only 1-3Watts which is enough for single cell-single LED,<6A typically, for anything more powerful it's a problem.
So,to get rid of heat at higher powers, one of ideas is to move that MOSFET somewhere else, where it can be better cooled. Simplest place for that is somewhere on LED board because it's well cooled and only one extra (Gate signal) wire is required compared to standard driver connections.
Next problem is that MCPCB with LED+MOSFET must be:
1.Isolated from core - MOSFET drain is usually also thermal pad, and since drain is not connected to GND potential, board must be electrically isolated from core - classical DTP boards are not allowed!
2.Have very high thermal conductivity - this is obvious requirement if LED current/power is high, to reduce LED die temperature and increase efficiency/lumen output
mosX boards are example of solution, they are isolated because they use anodized alumina ceramic as electrical insulator, and at a same time thermal conductivity is very high compared to standard non-DTP boards because alumina is good thermal conductor and it's much thinner than typical non-DTP laminated insulators. Thermal conductivity is not as high as on DTP boards,but it's close enough and mosX is good solution for multiple LED PCBs,where LEDs are usually not driven to its absolute maximum.