I have an oven style air fryer (this one by Oster as I live in Latin America) that's comparable to an Instant Vortex Plus in function from what I can see. It is truly an air fryer in the sense that the heating element and fan are at the top of the unit, not the back or side. I recently went to visit my parents and stayed for a couple of months, and they have a basket style air fryer that I used frequently. Here are the key differences:

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• Capacity: The oven style air fryer allows you to layer food on up to 3 different racks, so you can make more food or cook a meat and a side at the same time. You do have to switch the rack position on occasion though in order to get the food on the bottom to cook as evenly as that on the top. IMO, I think this is easier to do than shaking other foods. The basket style only allows you to cook in one layer if it is anything breaded, and you have to shake other foods.
• Function: The rotisserie on the oven style gives you the option to do a whole chicken easily. Worked great in mine. I would love to make a shawarma style spit roast in there sometime as well.
• Cleaning: Basket style wins here. Many models have a dishwasher safe basket that is easy to just throw in and go. At my parent's place, that was really easy, but as I don't have a dishwasher at home it didn't make as much difference to me when deciding which style to buy. To clean the oven style like mine (wire racks, not nonstick trays) you have to scrub them wish a brush and also wipe out the inside and door of the oven regularly to avoid build up. The cage for French fries is difficult to clean out well.
• Cost and Size: Most basket style air fryers are cheaper here. You can find a variety of models and sizes. Oven style tend to be bulkier and cost a little more.

All that said, I really love my oven style air fryer. My use case is pretty unique though, as I live in Latin America and use it mostly as an alternative to my range which runs on a propane tank and takes forever to heat up. I only use my gas oven now for big bakes (lots of cookies, cakes, and pies). In contrast, there's hardly a day that goes by anymore where I don't use my oven style air fryer.