You have come to the right place; we are always ready to help you spend money to meet code or safety or livability, as applicable.

I will help set requirements. Not having either brand or model of hood, I can only address requirements that each must have for "good enough" performance. You have two cost drivers that relate to island operation, and one due to the need for MUA. Let's address these in order.

Size. Ideally, one would set the hood to be just higher than one's head when bent forward to assure minimal head risk. Higher requires larger aperture area due to the cooking plumes expanding as they rise. 48 inches width for a 36 inch rangetop is an appropriate width for typical plume expansion angles (~10 degrees from vertical) with a bit of reserve for cross drafts. Cross drafts become ever more significant when raising an island hood above nominal height, so that is another issue one needs to have some confidence in containing.

An island hood mounted lower than 36 inches can likely live with a 27 inch front to back dimension (exclusive of char broiling, perhaps). For higher mountings one needs to go deeper, and I think 30 inches is probably OK if you aren't too tall. Otherwise, for any intention to set the hood at 40 inches or higher, the 34-inch unit will be better.

Flow rate. I usually recommend 90 ft/min for hood intake velocity at the hood aperture, based on searing and wok cooking at residential scales. However for char broiling, I would go with the recommendation of Greenheck (https://www.tagengineering.ca/wp-content/uploads/2015/02/KVSApplDesign_catalog.pdf) and call for 150 ft/min. You don't get a lot of averaging of the plume volumes with the small reservoirs of these residential hoods. (You may want to look at the thread started by @opaone at: https://www.houzz.com/discussions/5745986/commercial-range-hood-install#n=69 for how to save CFM with large reservoir commercial hoods.)

Consider the 48 x 30 inch unit. The area is about 4 ft x 2.5 ft or 10 sq. ft. This could need 10 x 150 = 1500 CFM for char broiling, requiring a blower rated somewhat higher -- perhaps 2250 CFM. Without the char broiler, the 90 ft/min requirement would lead to a volumetric flow rate requirement of 900 CFM and rated blower of 1350 CFM (somewhat dependent on hood pressure losses and MUA pressure losses).

You may observe that this lesser requirement is more in tune with the expectations of the hood designers. Once char broiling is called into the mix then the designers intent is defeated and a more robust solution is needed. For blowers rated higher than 1500 CFM, the duct should grow from 10 inches to 12 inches.

In addition, I would recommend that the blower not be in the hood, but mounted on the roof or outside wall, and a silencer be used in between. This will greatly reduce noise.

MUA. Whatever volume of air goes up the hood to the outside has to be matched by the volume of air introduced to the kitchen from the outside via whatever means are adopted, and in many locales heated when the ambient air temperature is cold. Many paragraphs can and have been expended on this subject, and I would appreciate your searching them out before asking about what is still unclear. Fantech makes MUA systems for residential use, as well as silencers.

First, some good reference info here: https://www.gardenweb.com/discussions/5161173/hood-faq

What you need depends on what styles of cooking you do, for how many people, how often in what environment and then what your goals are for Indoor Air Quality (IAQ - for both health and comfort), noise and budget.

There's a big difference in boiling water 3 times per week (most any hood will do) and pan frying, woking or char grilling 5 times per week. Char-grilling is possibly the greatest source of indoor PM's and VOC's from cooking of any style of cooking (I'd not have one indoors (even w/ our commercial hood) and I think you'd be hard pressed to find any medical folks who'd have one). We are only just recently learning how cooking itself (even on electric or induction ranges) is affecting our IAQ and health and in particular in well sealed houses.

There's a huge difference in Hawaii or Greece where you likely have doors and windows open and good outside ventilation and Minneapolis or Stockholm where your house is much more closed up and less well ventilated.

In short, with a char grill in an island I'd very strongly recommend a commercial hood system designed by one of their engineers (unless you are in Hawaii or similar). And FWIW, that is the first time I've ever recommended a commercial hood. Totally different story without the char grill.