If iron is really better than bronze in every way

It's the other way around: bronze is better than iron in almost every way. Mechanically, they are similar - similar hardness, and (if the iron is good quality) similar toughness. (Which one is harder depends on the tin content of the bronze alloy, and work hardening of the bronze and iron objects. How much the iron can be work hardened depends on the impurities in it.) The advantages of bronze are:

1. Bronze is more corrosion resistant. Iron rusts, while bronze usually develops a stable layer of oxidation on the surface (tarnish).

2. Bronze is easier to make (given copper ore and tin ore). The temperatures needed to smelt (i.e., convert the ore to metal) copper and tin are much lower than that needed to smelt iron. You need about 1100-1200C to smelt copper, about 1200-1300C to smelt iron. Further, the smelting temperature of copper is higher than the melting point of copper, so the product is liquid copper, which allows easy separation of the copper from the non-metallic parts of the ore. Iron is the other way around: the smelting temperature is below the melting point, and the smelting chemistry happens in the solid state (in a typical early iron smelting furnace). The product of iron smelting is a spongy bloom full of slag (the non-metallic parts of the ore) which needs to be gotten rid of. To do so, one hammers, folds, welds, hammers, folds, welds, and so on until the iron is clean enough. This (especially the welding part) needs to be done at welding temperature, which is very hot.

3. Bronze is easier to work. Bronze can be cast, while the temperatures needed for casting iron are prohibitive for primitive technology [1]. Bronze is cold-forged (with periodic heating and quenching to relieve work-hardening). This makes it much easier to forge large pieces, especially large thin pieces.

Iron, in turn, has one major advantage:

1. Iron ore is very abundant. In particular, bog iron is common, and can be collected without mining (and hard-rock mining with primitive technology (notably, without explosives) is very labour-intensive and slow). This means that iron can be much cheaper than bronze. For iron to be cheap, the skills needed for making and working iron, and the higher temperature furnaces required, need to be common enough.

Iron takes over from bronze because it is cheaper, not because it is better. Plenty of bronze continued to be made and used in the iron age (and we use plenty of bronze, brass, and copper today), and we see, for example, bronze armour (note thin sheets of metal, easier to do with bronze) used alongside iron weapons.

Iron does have one other advantage over bronze for weapons: the elastic modulus (Young's modulus) is approximately twice as higher, so for a given thickness and cross-section, an iron weapon is stiffer than a bronze weapon. This allows thinner long iron weapons, for a given cross-sectional shape, potentially allowing longer weapons of usable weight. This isn't as great an advantage as it might appear at first: since bronze weapons can be cast, it's easier to make stiffer cross-sections (e.g., blades with raised mid-ribs) in bronze than in iron.

Steel is superior to bronze and iron in terms of hardness. But making steel takes even higher temperatures than making iron (but not too high, or you get a puddle of cast iron at the bottom of your smelter, and until you learn what to do with cast iron, it's an unforgeable waste product). Steel technology is something that can develop within a mature iron industry.

why did it take so long for us to move on from bronze?

First, one needs to learn how to make iron. It's easier to accidentally discover copper smelting, while making pottery. If copper ore is used as a glaze, smelting can take place in the pottery kiln. Note that earthenware kilns get hot enough to smelt copper, but not hot enough to smelt iron. The accidental discovery of iron smelting takes hotter kilns (e.g., for higher-temperature forms of pottery than earthenware), or hotter-than-needed copper smelting furnaces. To reliably make iron, you need hotter furnaces. To usefully make iron, you need to learn how to get rid of slag from the spongy bloom, and learn how to hot forge iron, and how to forge-weld iron. All that, and you get a metal that is inferior to bronze (mechanically similar, but much more subject to corrosion).

More discussion by me and u/Antiquarianism in https://www.reddit.com/r/AskHistorians/comments/7ryt2v/why_was_there_a_widespread_bronze_age_before_the/ (my answer here is adapted from that earlier answer of mine).

[1] "Cast iron" doesn't need as high a temperature as casting pure iron (or steel). Cast iron is a saturated carbon solution in iron, and the carbon lowers the melting point. However, cast iron is brittle, and can't be used where toughness is needed. Cast iron can't be forged (without further processing to reduce the brittleness). The temperatures needed for casting cast iron are higher than the temperatures needed for casting bronze.

We are getting a lot of metallurgical answers in this thread, and while this is definitely a material culture question and the physical properties of the materials in question and the technological processes that go into making them should be a part of any good, comprehensive answer on the subject, let's remember that this is primarily a history subreddit, and the question is an historical one about the transition from primary use of one material to another.