Do you mean downdraft vs hood? Here is some information.

https://www.mrappliance.com/blog/2018/november/kitchen-ventilation-downdraft-vs-hood-fan/

You shouldn't worry about canopy vs under cab, and its great you can vent to the outside. What you need to do is measure your room, and calculate for the range (btu) you are trying to vent, plus the length/turns of the ductwork in order to determine the cfm that whichever hood you go with needs to be able to move at a minimum to clear your room.https://www.todayshomeowner.com/how-to-calculate-kitchen-range-hood-fan-size/ . It's always best if you have a hood that is the same width as your range, and isn't too shallow (but isn't a head banger either!).

10+ years here trying to teach fundamentals of cooking ventilation based on the extensive HVAC literature available, and there are still tertiary sources of information that barely rise above folk tales.

First, the most efficient hoods in terms of performance for their electrical costs will be those developed for commercial purposes; HVAC operating cost is one of the major costs for restaurants, for example, so inadequate performance won't be tolerated. From commercial hoods to residential hoods, "shortcuts" are taken to compensate for low ceilings, noise limitations, need for variable flow rates, reasonable duct sizes, aesthetics, and cost. Residential hood manufacturers design in a trade space pitting performance against cost against aesthetics, and at best, only two of these can be maximized for a given device.

In addition, as the goals for grease-free kitchen ventilation have risen along with the availability of higher performance (pro-style) ranges, the performance requirements have greatly increased from the decades-ago small hoods barely removing the steam from a boiling egg pot. As these performance requirements increased, another issue became apparent with the development of low temperature combustion appliances for hot water and household heating; they had such wimpy drafts that they were easily back-drafted when the flow rates of kitchen ventilation, now potentially installed in tightly sealed houses, increased to deal with serious cooking on pro-style ranges. Back-drafting can induce carbon monoxide into the house. This led to code requirements for deliberate make-up air (MUA) systems being required just as they are for restaurants.

For an overview of the issues as they pertain to commercial cooking, please download and review the Greenheck Guide at http://www.greenheck.com/media/pdf/otherinfo/KVSApplDesign_catalog.pdf. The first 12 or so pages may be sufficient. Note the arguments for the Greenheck approach to CFM requirements. These are ultimately determined by experiment for standard commercial hood designs, but can also be inferred from research on the upward velocities of cooking plumes as a function of burner/hob type along with cooking temperatures of various foods. The requirement boils down to having a sufficient velocity of air flow at the hood entrance aperture and thence the total CFM (air flow rate) needed to achieve that velocity.

We also know from plume expansion behavior that the hood should exceed the range size unless side skirts are used. (Side cabinets can help, but usually don't extend far enough from the wall for full effect.) Most don't want side skirts on their hoods. From this we have been using a compromise recommendation of a hood width 3 inches wider than the range top on each side.

So choose a sufficiently overlapping hood intake aperture area. For any serious use, choose baffle filter type hoods, preferably with some volume under the baffles for transient plume capture. Calculate the intake aperture area (sq. ft.). Multiply by your chosen velocity value for good containment; I recommend 90 ft/min. This is equivalent to 90 CFM per square foot of aperture. The product number is the actual CFM needed for hood ventilation and, roughly, also to be supplied by the MUA system.

Select a duct size that keeps the air velocity in the duct between 1000 ft/min and 2000 ft/min. This is not too significant if the duct is going to be 6 inches between the interior and exterior, but important for ducts passing through floors and attics.

All blowers likely to be used for hood ventilation have an actual flow rate that decreases with pressure loss. This is the reduced pressure on the intake side of the blower and increased pressure on the other. In a hood system, this pressure loss comprises the pressure not made up by the MUA system, the pressure loss across the baffles, and the pressure loss incurred by duct transitions, bends, and surface friction. Without knowing all of these losses as a function of flow rate, it is usually safe to specify a blower 1.5 times larger than the actual flow rate calculated earlier. This usually also applies to the MUA; however, without baffles but with characterized dust filters, the losses can be estimated better and compared with the MUA blower's fan curve to assure adequate replacement air to keep house pressure nearly equal to exterior air pressure. MUA requirements are also influenced by Code, nature of combustion appliances and any MUA they may be operating with, and house leakage.

Whether the hood is canopy type or (large) under cabinet type is not the issue. Ensure that whichever is more appealing can support the requirements.

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