I personally have never used the self clean feature. I'm too worried about the heat from that messing up the electronics (that's what people thought several years ago when I got mine; not sure if opinions have changed). I generally use some kind of pan to catch drips, so only rarely have things drip onto the oven floor, and for things like roasted chicken that may spatter grease all over, it seems to just bake off over the next times I'm using my oven. So, I can't tell you how the self clean works, but I can tell you that I haven't really ever felt the need for it, either.

I don't have the Bosch but I have the Electrolux, and they all work pretty much the same so I can answer some of your questions. Yes, induction ranges are very easy to clean because of the low heat on the cooktop. Unlike electric radiant smoothtops, it's very hard for stuff to bake on to the glass. Burners hot after using... it really depends on what you were cooking and for how long. The burners themselves don't get hot, but heat transfers to the glass surface from the hot pans. Sometimes it might be hot enough to burn you if you touch it immediately after cooking. But it gets much less hot than electric radiant smooth tops and cools down to a safe temperature much more quickly. The heat spreads away from the burner much less. Yes, you can put paper under the pans but you do have to be careful. I have used paper towels with success in the past, but when cooking with very high heat I have seen them get singed. No clicking sounds while cooking, but at high power levels I get a small buzzing noise from the pans sometimes. Nothing bothersome. Induction burners don't glow red or anything while they're on, but the range will have indicators to let you know if a burner is unsafe to touch. They might be "Hot surface" lights, or it might display an "H" or something in the burner display after you turn it off. Can't speak to the Bosch specifically but on every range with electronic controls I've ever seen, it displays only the clock while not in use, though that can be turned off. On all the ranges I've seen with backlit buttons (mine included) they turn off while not in use.

I have a Wolf induction cooktop (model before the bridge model) over two Wolf ovens. Love the way the induction and ovens work. As for induction, there is probably a lot of similarity in the way the hobs work between manufacturers if they have the same power, but the bells and whistles (e.g. how many timers, number of increments for each hob) may make a difference to you. However, the ovens are a completely different matter. Wolf ovens are by far the best cooking ovens I've ever had. Recipes that I've made for years turn out SO much better in the Wolf ovens (my husband keeps asking if it's a new recipe!). And Wolf backs its products up better than anyone else. Good idea to match the cooktop and ovens.

On the point of durability/reliability as a factor: Athough this is good point to consider, I'm not sure how much we can really say about the Bosch slide-in gas range being or not being more long lived than the freestanding Electrolux induction, nor how much longer lived it might be. The hope is that a gas range without much in the way of electronics for the burners will have less to fail and therefore last longer. Still, the big uncertainty is the result of of the prevalence of electronic control systems in all kinds of major brand ranges. All seem prone to some early failure and to reflect susceptibility to issues with high-heat self cleaning cycles. I have to say, that a lot of the discussion that I've seen here about longevity of gas versus induction has been about gas ranges that are premium-priced pro-style ranges and re-conditioned vintage ranges rather than major brand gas stoves. I sometimes see citations to statistics garnered and reported by the National Assocation of Home Builders and Consumer Reports which were indicating 11 year lives for electric ranges and 13 year lives for gas ranges. Turned out, though, that those statistics were about replacement rates rather than appliance life expectancies. Plenty of folks remodel and replace functional ranges for something they regard (or hope) will be better. On the comments, "I can get a slide-in model that I like and I prefer the appearance over a freestanding" and "There is no slide in induction range that I like not to mention the price differential." Choosing any stove is inevitably choosing a mix of compromises of design, engineering, and budget. Induction burners are just one of numbers of factors to consider. How you weight that factor along with all the other considerations may be different than how I or most others else here might weight our own preferences, priorities and/or prejudices when choosing a stove. My own aesthetic preferences run to old-fashioned appliance white with a tolerance for stainless steel and general distaste for black casings. Yours are the opposite. My preferences are not "better." They are just what I prefer. So, I say, have confidence in your own priorities and your own budget. When you are paying as much for a stove as these cost, aesthetics are a valid consideration. Re the comment: "Even more burner/hob control than gas - seems like it would be better at lower heat levels such as simmering." Another set of tradeoffs rather than clear choices of one being intrinsically better than another. I'm not sure that that there is necessarily better low heat "control" with the Elux freestanding. There might be, might not be for you. Depends on what and how you cook, what you cook with, and what your preferences are. While the Elux burners have more low-end stepping than on most induction ranges, the settings are still digitally stepped. The Bosch burners have "analog" adjustments which are theoretically infinite. Do we really need infinite adjustability? Some of us want it. Others of us find there are enough steps in digital controls for what and how they cook. There are a number of OTOH tradeoffs beyond this. With a pan that is matched with burner size, an electric burner will deliver heat more evenly spread across the base of a pan. Spread is one thing. Steadiness is another. Depending on how the power cycling works, the heat may or may not be steady. With induction burners, you will have a small circle in the center of the toroidal induction field which is outside the field and where you depend on the pan construction to spread the heat. On the induction burners on most ranges, including the Elux you are considering, heat cycling is very even and steady, so you won't see power cycling in pan liquids. (Not so much applicable to some Whirlpool ranges and cooktops which reportedly have cruder power cycling rather like that on many portable induction cookers). With the Bosch gas burners being capped rings, you also get a toroidal effect in heat delivery and it can be more pronounced than with induction at very low heat levels. Again, a pan's construction may spread the low heat sufficiently evenly to the edges and to the center. Otherwise, when you put a pan on a small gas burner and turn the heat way down, you may find the low flame concentrates the heat towards a small area in around center. No big deal for simmering liquids but maybe a problem with things like delicate thickened sauces or chocolate where having the flame concentrated towards the center. Depending on your pan's construction and how you want the heat controlled, you might or might-not find yourself wanting a flame tamer plate. Another OTOH is that the Elux digital control make it very easy to exactly repeat heat levels when you figure out the ones you want to use. With gas, you have to eyeball it every time. At least I do with the gas that gets delivered in my town. (We are near production fields but get last choice, so the quality varies.) This is why I prefer my induction burner for my pressure cookers. Are any of these big problems? Maybe. Maybe not. They seem to have been concerns for some posters here. The concerns might or might not matter for your own cooking and interests.