What can a centralized government do that an "uncentralized" government (like that of the United States under the Articles of Confederation) cannot do, concerning trade, taxes, defense, and the enforcement of laws? Contrariwise, what advantages does a decentralized government have over a centralized government?
Some of the advantages aren't strictly speaking related to government per se and apply in other contexts:
Centralization can increase efficiency
The more de-centralization, the more inefficiency. Each part of federation will do things their way - often, at cross-purposes or actively contradicting what other parts do.
In pure economic terms, bigger means cheaper and more fiscally efficient. You have less overhead (one set of support staff - even if slightly bigger - per task - vs. multiple sets in each piece of federation). This is why companies used to like M&A.
Economic benefits of centralized monetary and economic policy
Economy is weaker due to mismatched currencies AND protectionist tariffs.
There is no power to enforce any decisions on dissenters.
7 states vote to have a war. 5 states dissent. Only 7/12th of the army is deployed, since nothing forces the dissenting states to follow that vote.
11 states vote to have a high tax on millionairs. 1 state dissents and doesn't obey that vote. All the millionairs move to that state, depriving the other 11 states of tax revenue they expected and overwhelmingly voted for.
Times sensitive decisions are much slower (and worse, less likely to arrive in the first place).
Governing by a committee (parliament) has its place in slow moving circumstances. Prosecuting a war by committee... Not usually a good process.
So, the US is still not a Centralized State under the Constitution. It's still decentralized, but the central government is more powerful. To understand the differences, lets pretend that all 50 U.S. States are in fact nations unto themselves.
The Articles of Confederation organized the United States as a Confederacy, where the States had strong authority and the central government had as much or weaker powers than the States. Essentially, the things a central government needed to were powerless to do (The big one was the founders were really worried about having a Standing Army so it was near impossible for congress to raise one... which turned into a need to have one when the Whiskey Rebellion happened.). Confederacies in general are more like treaty organizations between a bunch of Countries. The Central Government may negotiate international treaties but the member states will all have to ratify them. The other problem with Confederacies is that they typically have a De Facto right to leave the Union. The EU is probably the best extant example of a Confederacy. The Swiss Confederacy, despite the name, does this by Direct Democracy. Each Canton (similar to a U.S. State) can at anytime have a referendum to leave... they just don't like the idea, and the term is basically an artifcact from when it was a legit confederacy.
The United States is a Federation which has a stronger Federal Authority but is restricted from meddling in certain affairs of the member states. As such, citizens of a Federation have will usually be under Dual Sovereignty... they are both citizens of their state, and their Federation. For example, Every U.S. Citizen is under U.S. Federal Jurisdiction, but Florida Man is not under California Jurisdiction. The U.S. Federal Government is bound by the constitution to certain duties only (a military, the regulation of commerce between states, and the ability to make foreign deals for all of it's member states). Member States of a Federation do not have the right to leave the Federation (The U.S. had a big war over the matter). While not all things are given to federal governments equally (For example, in the United States, immigration is handled by the Federal Government. In Switzerland, it's handled by the Cantons.
We also have Devolutions which are the reverse of Federations. Basically Devolutions are created by a Unitary State that decides to create regions within its borders and grant them self-government elements like Federations. The United Kingdom is an example of a Devolution as it's made up of Britain, Wales, Scotland, and Northern Ireland. The big difference is that the Central Government can reform these member states or even revoke the region entirely. Other examples include Spain and Indonesia. Basically, they have self governance at the pleasure of the central government. A U.S. example would be the relationship between the states and it's counties.
Finally, there are true Unitary States, like France, which have one Central Government manages the laws for all the nation. Local communities are placed in regions with determines representation and the civil servants charged with running the local governments functions in the area. In the U.S. States are essentially Unitary States for a comparison point.
A strong, centralized government has some very useful traits. The ability to centrally establish policy for an entire nation. This can be a powerful force and has literally pulled one of the largest nations on the planet out of poverty and in the past, pulled entire nations out of the dark ages.. as the Soviets did. China and the Soviet Union are of course, the more extreme of centralization. But the Soviet Union was unique in that it accomplished quite a bit.
Centralization of power also allows for a more direct and speedy response to larger threats.
.. and this is the most important point in my view. I linked to a report about Climate Change and we are currently looking at a catastrophic change in the environment of this planet. We would need a GLOBAL centralized power to deal with this. However, the world's governments are largely de-centralized and thus, there's little action because everyone is pursuing their own interests. Which in turn, means zero focus on the damage we're doing to the planet.
The most extreme version of centralization would be a world government. There's definitely a lot of dystopian stories around such an idea. However, it's likely the only answer to the current climate crisis.
A strong centralized government can be a force for good and change. However, it can also be an authoritarian nightmare and governments are just tools. It's how the people(s) use them which creates brutal regimes.
Decentralized governance, in my view, has few benefits. You have more local autonomy, but you'll always be out-competed by larger more efficient entities who can take advantage of collective action. Brexit vs the EU is an excellent example of this. Where the UK, now "free and autonomous" can trade on its own terms. Which can lead to some challenging negotiations with the EU. the reality is a central cooperative authority like the EU can spread the burden, while the UK is going to be hit much harder.
Human societies have been consolidating governance since the beginning of time. If I can just pedantically break it down...
We started with tribes, then we went to city state, then empires, then nation states. The next step will naturally be global governance. Because being able to rally resources at a moment's notice is a very powerful thing.