There are lots of threads on this, if you search you will probably get alot more then I am about to tell you.
Suspension lifts are alot better and alot more expensive. In a nutshell they lift the entire truck off the ground using upgraded parts, where as a body lift only lifts the "shell" the body of the truck from the frame. So with a body lift you gain no frame clearance but you gain body clearnace. With suspension you gain both.
Suspension lifts enhance your off road capability and body lifts dont. They are not a suspension upgrade.
There are no disadvantages of a supsension lift besides the cost. Body lifts only do the job half right but cost a few hundred dollars.
2002 XLT 4.0, 3"BL, 295/75/16 Nitto Terra Grapplers, K&N FIPK, XCAL 2 w/LaSota Racing Tune, 2 12" Alpine subs, Alpine Deck, Cobra CB, Low Pro Tool Box, Straight Pipe Exhaust, Blacked out heads/corners, Expo OHC/Dome/Cluster, etc...
2011 F-150 XLT, 5.0 Coyote, Hell Bent Steel Leveling Kit, 15% Tint, Flo-Pro Super V Exhaust, MA Audio 1000w amp, 10" Sony Sub