LED lamp fixture:
This is the standard LED grow light type and the one you’ll see most of online. It typically has a plate or aluminium body (housing) and inside there are drivers, fans, wiring, possibly a heat sink, and a board with the light emitting diodes. Some of these LED lamps come with focusing lenses or covers on top of the diodes. These lamps come in all price ranges and the price is primarily determined by how big the lamp is, how many diodes it has, and what the build quality is. They come for as cheap as $60 but a decent lamp that will illuminate a single plant well, will cost around $100. The more plants (or the larger the grow area) the bigger/more lights are required. For a 3×3’ (90×90 cm) area or approximately 4 plants, 2-3 lamps (~$300) is necessary. The more light, the bigger harvest (to some extent).

Pros:
Usually sturdy construction and not easily damaged.
All the electrics and wiring is safely tucked away inside the body.

Fully assembled lamp.

Easy to use, good for beginners.

Cons:
Cheap lights are usually built with cheap materials and could be a fire hazard.

The cheaper the light, the lower quality and lower efficiency are its parts (drivers, diodes, fans).
Depending on size and lenses, its light footprint (coverage) could be poor.

Are often marked with inaccurate or inflated specifications.

COB (Circuit on Board): 

To put it simply, a COB is a “cell” that consists of a large number of tiny, tiny LED diodes. Each diode is typically 1W and COBs come in all sizes. There are 10W COBs (ten 1W diodes making one 10W COB “cell”) all the way up to several hundred watts COB. Good brand COBs, such as Cree and some Bridgelux (Lumilux?) models, are very efficient (high efficacy) but due to the higher concentration of diodes on a small area, they generate a lot of heat per area. The heat dissipation is solved by heatsinks. The bigger the wattage, the bigger the heatsink as heat generation is proportional to consumed watts. While the COB cells weigh almost nothing, the heatsinks on the other hand are made of aluminium and add a decent amount of weight.
A COB lamp typically consists of a single COB cell attached to a heatsink, and a driver. As their build is fairly simple, this is a popular DIY lamp type for handy tinkerers.
Sometimes COBs are apart of standard LED lamp fixtures where a few COBs supplement a larger number of smaller, standalone diodes. 

Pros:
Good brands are very efficient (high efficacy). 

High light output.
Extremely low risk of failure due to no moving parts (passive cooling through heatsinks).

Cons:
Concentrated light footprint: high PPFD values in center spot but low PPFD away from center resulting in multiple COBs required for an even footprint (coverage area).
Can be heavy and bulky depending on the size of the heatsink.
To get good results with COBs, a fair understanding of light, PPFD, and light footprint is necessary (not suitable for beginners).

Sensitive to mishandling and physical damage.

Quantum Board (QBs):

The name, somewhat misleading, is not quantum physics related. A QB LED light is actually quite simple. All it is, is an aluminium board (and a bit of epoxy and copper) with light emitting diodes on one side and, most commonly but not necessarily, a heatsink on the other side. QBs are powered by a driver that is either fixed to the heatsink or just sits loosely on top of the heatsink. You could say that a QB is similar to a COB but with a larger area. Instead of a small COB cell, a QB uses the a larger aluminium board. The most common size for a single board is about 12×9” (30×20 cm) with a thickness of 1.5mm (0.06”). 

The entire QB concept is to have as few parts on the fixture as possible to keep weight to a minimum but also reduce the cost of any unnecessary parts. QBs do not have any housing which means the diodes are completely exposed and prone to damage if handled carelessly. No fans are used either as the goal is to maximize the lamp’s efficiency (efficacy) at turning electricity into light.
(A somewhat accurate comparison between a standard LED light fixture and a QB would be like comparing a pickup car to an F1 car. The pickup is comfortable to sit in, it’s user friendly, convenient to load stuff into and has all kinds of safety features, but it’s gas-guzzling and not very efficient. The F1 car on the other hand is built for performance and speed and has very few, if any, practical everyday features.)

Pros (very similar to COBs):
Good brands are very efficient (high efficacy).
High light output and decent light coverage.

Extremely low risk of failure due to no moving parts (passive cooling through heatsinks).

Cons:
Breaks easily if dropped as it has no covers for the diodes.

Some electrical wires are (typically) exposed.

Some brands sell QBs in parts and require some assembly.