The distinction is between a "federal" system of government and a "unitary" one. Both have been tried, some of have been toggled between, and there are pros and cons to each.
For example, France historically had a unitary government in which prefects appointed by the central government had authority over issues that are provincial or local government tasks in many other countries. For example, if you wanted to change the speed limit on the road through your village you would need approval from the local prefect and would have to lobby a member of the national parliament to make that happen. In the 1980s or so, it switched to having regional governments with internally elected officials.
Benefits of Unitary Government
One benefit of unitary government is that resources aren't wasted on meta issues of deciding which level of government handles which issue.
Another benefit of unitary government is that it is less prone to NIMBY issues in which local governments adopt policies that have negative externalities or prevent something that is useful to the nation from being located anywhere at all. For example, Japan's unitary government has been noted for having better land use regulation than countries that vest that responsibility at the local level.
A third benefit may be that the supply of competent potential elected officials and senior government officials may be scarce. Your nation may have enough competent people to serve in elected office and senior government offices to run one national government reasonably well, but not enough to run dozens of provincial governments as well.
More generally, if the most competent elected officials and government officials are in the national government, then important policy decisions are made by the most competent people available.
A fourth benefit is that it is easier for people new to democracy to understand a unitary system than a more elaborate federal system.
A fifth benefit is that policy changes can be imposed nationwide very rapidly. But, the downside is that getting a policy change to happen may be harder with a national legislature to convince and greater inertia than with a smaller provincial body to convince. It also makes it easier to research the law that will apply to anything (especially interstate commercial ventures) if you have only one body of law to review.
A sixth benefit is that there may be some provinces where the locals are prone to elect unwise provincial leaders who would adopt bad policies. But, their voice is diluted in a national government so their bad policies are not implemented.
Benefits of Federalism
One of the practical purposes of a provincial level of government is to prevent too much of importance from riding on a national government deadlock.
For example, in the United States, now and then, there is government shutdown because a majority in Congress cannot agree on a budget. If all government activity depends upon that budget, then all government activity comes to a screeching halt, nationwide, when there is a failure to agree on a budget. But, if lots of important stuff is funded at the provincial level, then only the stuff funded at the national level stops nationwide when there is a failure to agree on a budget. Of course, there could be a failure to agree on a budget at a provincial level too. But, only one province is affected at a time.
Similar logic applies in the case of a strike by a public employees union.
A somewhat related concept is that smaller bureaucracies may simply be easier to manage.
A second purpose of a provincial government is the serve as a "minor league" training ground for future national parliamentarians and senior government officials. Rather than electing novices to the national government, voters selecting national elected officials and national governments selecting senior executives can choose from people who have distinguished themselves in their service in very similar positions at the provincial level if they wish to do so, and novices serving in provincial government do less harm.
A third purpose of provincial government is to put more of government into the hands of governments that aren't truly sovereign. A sovereign government has no "safety net" of higher level judicial officials and legislators to correct them if they take action that is beyond the realm of acceptable political conduct. Provincial government officials recognize that they can't start wars, change boundaries, change the national constitution, or violate their own constitutions and get away with it in the manner that national governments do. There are plenty of people who have something worthwhile to contribute to the policy process who shouldn't be trusted around the power to make war, for example. This feature also means that most national officials, having been trained to act within limits in the "minor leagues" are less likely to push beyond those limits when they eventually take national office.
A fourth purpose, usually put higher on the list by political scientists, is that different provinces can have different policies. For example, gun control restrictions that might make sense of a highly urbanized province might not make sense for a province in a huge arctic desert where police are not readily available and wild animals are a genuine concern. Or, different provinces might have different ethnic and religious makeups that call for different policies - one province might regulate alcohol very strictly while another might allow it rather freely, for example.
The differences need not be strictly differences of policy either. For example, if residents of one province speak French and residents of another province speak German, it may be useful to have two different provincial governments even if they are applying a single set of laws.