Forging Advantages
Forging is frugal with material. Forging also allows access to steels found in shapes not usable as is. Forging is the only common way to get damascus or wootz, if that is what you want. Forging also lends itself to some shapes that are difficult or expensive to reach using stock removal, such as highly curved blades.
Stock Removal Advantages
Speed-stock removal is pretty quick for small and medium size blades. Stock removal makes more use of stainless and high alloy steels. These steels can be forged, but the more complicated they are, the more difficult it is. Stock removal is less costly for initial setup. All you need to start is steel, a hacksaw, files, some sandpaper, the number of a good heat treater, and a 55 gallon drum of elbow grease. My first blades were made from O1 steel using grinding belts from Home Depot on a 1 x 30 belt sander.
Forging is surrounded by a lot of misinformation, such as edge packing, grain breaking, myths about what a forged blade can do that cannot be done with a stock removal blade, something about forging in a certain compass direction, etc. Sorting through it all is sometimes a disadvantage in itself. Just because a blade is forged does not make it better.
Bear in mind that nearly any steel used by a stock removal maker has been extensively hot worked before the maker gets it. This has usually been done in a hot rolling mill. In this sense, stock removal steel is "pre-forged" when the maker gets the pieces. Exceptions exist, and some makers use steels in the as-cast condition, taking them out of a mold, and giving them a final shaping and polishing.