What is the advantage of a steel skillet over a cast iron one? I currently use cast iron for most everything and am curious what I might be missing.
Pan sauces made with wine, vinegar, or any other acid are better in stainless steel. If you put any acid in cast-iron, you are harming your seasoning, and leeching iron into your food. This will affect the taste of your sauces, I find pan sauces taste metallic when made in cast iron.
Stainless steel also heats up and cools down much faster than cast-iron. This is great when you need quick heat, or fine control of your heat. You can also plunge a piping hot stainless pan into an ice-bath without cracking it in half.
If there's an advantage to getting a steel skillet as well, what would be recommended?
Go with a a bonded stainless-steel pan with an aluminum core. The most well known manufacturer is All-Clad. The stainless steel exterior is great due to it's non reactivity, you can literally put anything in it. The aluminum core distributes the heat much more quickly and evenly, minimizing hot-spots.
Is a steel skillet good for cooking omelettes?
Not in my opinion. I go with a non-stick pan every time.
I have to recommend sticking with a nonstick pan for eggs. There's simply nothing better, although well seasoned cast iron comes awful close. If you're spending more than $20 for a nonstick egg pan, you're doing it wrong. You don't need Calphalon, or any other big name for a good nonstick pan. Go to a restaurant supply store if you can and buy a cheap one there. With care it should last you 2-5 years depending on use. I found my current one at a Bed Bath & Beyond.
The biggest practical differences are going to be:
Nothing sticks to a well-seasoned cast iron pan. Everything sticks to cast aluminum, even the brands that call themselves non-stick. (I know because I've tried a few of them.)
While it's true the cast iron can crack, rust or chip if not properly cared for, aluminum is reactive and scratches easily, and even if you get one of the newer anodized ones, you lose the benefits of that as soon as the surface starts to chip and peel (which it will). Cast iron will last much longer when properly maintained; I've seen some that are decades old and heard about some that are more than a century old.
Aluminum has better conductivity and will, in theory, provide more even heat than cast iron. However, every cast aluminum vessel I've ever used has had major problems with hot spots. Basically, both are poor choices in this respect, except in the oven, where hot spots are essentially a non-issue; if your oven is like mine and the element turns on and off to maintain temperature, you'll get much better results with a cast iron dutch oven because it will hold its temperature while the element is off.
Cast iron also works great with induction cooktops, aluminum doesn't work at all. [Cast] Aluminum really works best on standard metal cooktop stoves, although it's okay for glass as well. I say okay because most glass cooktops tend to have elements that go on and off, so depending on your particular stove, this might lead to uneven heat when using any kind of aluminum.
Cast iron is heat-resistant. You mention the melting point, but it's more complicated than that; make sure you check the specifications on whatever cast aluminum you're thinking of buying, because a lot of it isn't even oven-safe (and if it is, it's only safe up to 400° F or so). The term "dutch oven" can be quite a misnomer for those pieces as they can easily warp or crack at high temperatures. Spun aluminum is obviously much worse but cast aluminum is only marginally better.
On the plus side, cast aluminum is obviously much lighter than cast iron and requires less care. Enameled cast iron is also easy to care for but is obviously much more expensive than both regular cast iron and cast aluminum.
In your case, it would seem that your two primary requirements (caramelizing sugar and roasting meat) are at odds with each other. For roasting, you want a very steady, even heat. For caramelizing sugar you need precise control, you need to be able to reduce the heat very quickly when you hit the melting point. Cast iron would be absolutely terrible for caramelization, but is a far better choice for roasting.
Personally, I use a regular (non-enameled) seasoned cast iron pot as a dutch oven and just use a small light stainless steel saucepan when I need to do something like caramelize sugar. I'd suggest you do the same, unless you're really low on space and genuinely need one piece of cookware to do it all.
Honestly, the only thing that cast aluminum really has going for it is its price. The ease of maintenance is overshadowed by the fact that the pieces don't tend to last that long, and everything else it's good at is handled equally well or better by stainless steel with an aluminum or copper core. The few pieces of aluminum (or cast aluminum) cookware I still own tend to sit at the bottom shelf at the very back and gather dust, but YMMV.
Best Answer
Ok, so the "Smart XXX Alec" in me wanted to start out by saying: "The French oven is more arrogant and less useful." But I refrained until I learned I was right.
Looking at these two similar products Dutch Oven vs. French Oven I notice that there is not much difference except that the "French Oven" is 4 times the price & only good to 350 degrees in the oven where the Dutch Oven is rated for 400 degrees (F).
So I think I have to stand by my original thought.