It’s impossible to generalise about the devolution of power in the EU. Looking at the UK alone, for example, there is the parliament of the United Kingdom. Below that there are separate parliaments or assemblies in Scotland, Wales and Nothern Ireland (but not in England). A different range of powers and responsibilities is devolved to each. Below that each country within the UK has an entirely different structure of local government bodies, involving any or all of (in descending order of size) regional councils, county councils, district councils and parish councils. Stick in municipal corporations and town councils somewhere there as well. All of these bodies are elected. They deal with a variety of issues. They have a variety of revenue-raising powers. They are subject to various degrees of control by national or central government over what money they can raise and what they can (or must) spend it on. And that’s just within the UK. Other structures will be found in other European countries.
(And, in response to your specific question, issues such as zoning and local transport will be addressed at the level of local government, not central government. But the powers of local bodies in this regard – e.g. whether the local government has the power to operate bus services or merely to licence service operators – are usually decided centrally. Revenue-rasing powers vary from country to country and from authority to authority.)
It is interesting to look at what issues are controlled from the centre in the US and the EU respectively. The OP mentions the death penalty but, for the purposes of an argument that the US system is superior, this is not a good example. The US has long accepted that issues of basic human rights are the concern of the central government – hence the Bill of Rights. For a period, as has already been pointed out, the death penalty was prohibited by federal law (specifically, a Supreme Court judgement) in the US, and other issues of penal and police policy – the rights of accused and suspected persons, the prohibition on “cruel and unusual punishments” - are still very much the concern of federal law. The difference between the EU and the US is, crudely, that the US does not regard the death penalty as a matter of fundamental human rights, while the EU does. But that has nothing to do with attitudes to contralisation versus devolution of power generally.
An interesting point to look at might be the US attitude to road safety. On the face of it, this looks very much like an issue for the states, but the federal government manages effectively to mandate speed limits and legal drinking ages by threatening to withhold federal highway funding from states of whose laws on these matters it does not approve.
Areas of trade and commerce are also interesting. In the US, commerce between the states is a federal matter, but commerce within any state is a state matter. In the EU, reflecting its origin as a free trade bloc, the EU authorities have very considerable power to legislate in matters of trade and, reflecting the nature of the EU as a single market, no distinction is made between trade between member states and trade within member states. Those who object to the “bureaucratic interference” of Brussels will typically, for example, be objecting to a requirement to display prices in metric units (e.g. to show the price per kilo rather than the price per lb.) and they see no reason why the UK (for instance) should not retain the imperial system. In principle a US state might be free to move to adopt a system of weights and measures unilaterally – I don’t know – but in practice it is unthinkable. And in the EU member states are still free to adopt their own monetary policy and issue their own currency (and several do so), which is certainly not the case in the US.
In any federation there will always be tensions between the centre and the regions, and this will reflect itself in a not always coherent approach to the distribution of powers and responsibilities. It should not surprise us that different federations have different experiences, and end up with different distributions of power and responsibility. History and culture has a lot to do with this. But it is dangerous to conclude that, because two federations have different experiences and end up with different distributions, one is more “democratic” than the other.