Definitely look at induction. It has many of the advantages of gas - instant response, variable settings, etc without a flame. It is much easier to clean than standard electric even though the surface is the same due to surface not getting as hot. I am not sure best ranges as I have a cooktop and wall ovens.

I'm another induction cooktop fan. I don't have a range, so I can't speak to that particular combination. I got mine about five years ago. I had an all electric kitchen but also a propane tank for gas heating. I could have converted to gas, but didn't want to. I've had gas before and I felt the properties of induction were either as good or maybe even better for my particular situation. I read a lot about induction online and on the GW Appliance Forum. I bought a small Mr. Induction one-burner hot plate type gizmo to try out the concept. At the time I made my purchase induction was just coming into vogue here in the US. Very few major manufacturers had models available at that time. Many of the Appliance Forum folks who bought induction cooktops, imported them. I didn't want to do that. So when Kenmore introduced their 30 inch model, I immediately placed an order. I think I was the first person in my county to purchase one. I really like using it even though my model has very few "bells & whistles." I know that newer models have many more features. But after using an induction cooktop for the last five years, I don't think I could go back to either regular electric or even gas.

I would switch to induction.

Vocabulary can be a slippery thing. From your photo and your budget, I'm guessing that you aren't actually thinking about a "stove" or "range" -- at least, not as those terms are usually understood around here. Am I correct that what you want to do is yank out that radiant electric downdraft cooktop (Jenn Aire?) and drop in a 36" wide induction cooktop while adding an overhead vent? Also, am I correct that budget of $3k has to cover both the cooktop and vent hood? If so, I have some suggestions for things to consider. First, cooktop cutouts sizes vary between model years and brands. You might be able to open up the cabinets and drawers in the island and find a way to measure the dimensions of the existing cut-out from below. Or, take your cooktop's model number and do an online search for a pdf of the install instructions which will have the dimensions of the cut-out. Then, check those specs against the specs for the induction cooktops you might be considering. Depending on the particular induction cooktop you are considering, it might: (a) fit in the existing cut-out; (b) you might have to trim one or more sides to enlarge the cut-out (which means budgeting for the work unless your countertop is something other than the stone it looks like in your photo and you have the diy skills and tools to make the necessary cuts); or (c) the existing cut-out may be too big for some induction cooktops, in which case you have to figure out how to (and budget for) build up the rim support under the cooktop. Second, I'm recalling that some of the older Jenn Aire radiant electric downdraft cooktops were actually 42" wide. Is yours one one of those? If so, it rather narrows your choices of induction cooktops. All of the 42" induction cooktops --- at least all of the ones that I can think of off the top of my head --- are from expensive brands like Miele which will eat up most of your $3k budget. If your present cooktop is a 42" model, you might consider going with a 36" model and have some sort of cosmetic and structural cover fabricated (maybe in stainless steel) to cover the gaps and provide support. I'm guessing a new countertop for the island is not in the budget. Third, Green Designs mentioned a possible need for an electrical upgrade. Here's what that means if you did not understand the comment. Some 36" induction cooktops can run on a 40 amp circuit but many require a 50 amp circuit. Not so many years ago, 36" radiant electric cooktops might only have been wired to a 40 amp circuit. Seeing the existing downdraft radiant cooktop makes me suspect that the existing electrical circuit probably is a 50 amp circuit. Only you or an electrician on site can determine whether that is the case. You need to verify that you already you have 50 amp service (checking the circuit breaker may be the fastest way to do that). Otherwise, there are not many 36" induction cooktops that now are rated to run on a 40 amp circuit. Frigidaire comes to mind as one, and worth considering in light of your target budget. Fourth, the vent hood is going to be more expensive. As Jaykaym says, the Home Depot unit is out of consideration because it is a wall hung model. The linked Cavaliere is an island hood but it is only 30" wide, which is too narrow for your cooktop. At least, look at the 36" wide model. The basic problem you have to solve with any hood is that steam and etc. spread out as they rise. Think of the plume of cooking effluent as an upside down cone that gets wider as it rises. You want the hood wide enough to capture as much of the plume as possible. so that the fan grabs as much of the plume as it can. Too small a hood and, no matter how powerful the fan, you will be raising the plume up higher and spreading some of it further around the kitchen. Lots of very detailed advice here on fan and hood sizing over the years (particularly from Kaseki, our resident vent guru) if you care to search for details. The rule of thumb around here for decades has been that you want the hood to be at least three inches wider in each dimension than the cooktop it hangs above. With a 36" wide cooktop, the standard advice is to look for a 42" wide hood. You can go narrower with a wall mounted hood because the backwalls and cabinets to help confine the rising plume. No such aids for an over-island hood. That said, budget constrains your choices, which likely means looking at something for $100 more, such as the 36" version of the hood in your link. It will be better than nothing and, indeed, will be noticeably more effective than the existing downdraft unit. Be aware that running a 900 CFM fan into a 6" duct will be considerably noisier than better (but maybe less affordable) choices. Fifth, speaking of that 900 CFM fan, have you looked into make-up air (MUA)? Do you have any gas appliances (say, furnaces or water heaters) or fireplaces? Unless you have an adequate source of MUA for what your hood is sucking out of the house, running a strong vent fan can backdraft copious amounts of carbon monoxide into the living spaces. Also, more and more localities are adopting code provisions that require MUA for range hoods with fans rated to draw 400 cfm or above. Best check your local codes before anbody starts cutting holes in the ceiling and roof.