So, there are a few different issues going on here which are related, but distinct, and which historians have described using similar terminology, so it's rather confusing, but I'll attempt to cut through some of the confusion if I can.

Firstly, there is the question of 'state formation' which had been ramping up in monarchies such as England and France for a while by the seventeenth century. This had many facets such as the development of better bureaucracy and networks of communication for spreading royal influence and collecting tax, the expansion of local courts and magistracies, and the development of banking to fund the development of these emerging states, and their military expansion both in Europe and overseas. These, I would say, are some of the ways in which European polities were 'more of a state' in the 17th century than they were in the 15th (although this process had already started in certain respects by then).

This process, however, wasn't straightforward or linear, and was entangled with the reformation. While, broadly speaking, the early modern period saw secular authorities seize power from religious ones, this also resulted in many brutal civil wars and wars of religion in England, France, and most devastatingly in (mostly) Germany in the Thirty Years War. These conflicts we're neither straightforwardly secular authorities v the church, nor Protestant v Catholic, but all contained elements of both these phenomena. Sometimes, monarchs successfully seized power and wealth from the Catholic church by turning to Protestantism, such as in the case of Henry VIII, although a century later, Charles I lost both his power and life, in part, because he wasn't seen as sufficiently Protestant, which illustrates how messy this process could be. Others, like Louis XIV, successfully appropriated much of the power of the Catholic church for the state while remaining a Catholic king.

So, to actually answer your question, two significant ways in which Europeans kingdoms were 'more of a state' in the 17th century than the 15th were, firstly, improved bureaucracy, communication and finance, and secondly, that the state had, in many cases, gained in power and authority compared with the church.

However, just to confuse things again, I don't think this is precisely what is usually meant by the concept that the Treaty of Westphalia marked the start of the age of nation states. Firstly I should caution that this idea is rather outdated and not universally accepted by historians, in part because most post-Westphalian states were not really 'nation states' at all.

However, having said all that, I do think the idea has value, and I will try to now explain why.

The Thirty Years War didn't really increase centralised authority, it weakened it and left much of Europe in chaos.

However, what the Thirty Years War and the Treaty of Westphalia did do was mark the end of any pretences that supranational institutions (which is an anachronistic way of phrasing it but is the best way I can think of right now) could impose their dominance on the rest of Europe.

The Treaty of Westphalia demonstrated the failure of the supranational ambitions of the Papacy and the Hapsburg Empire, and indeed, any ideas of a pan-European protestant revolution. It marked official acceptance that the Hapsburg/Spain/Catholic faction would not be able to reassert it's dominance over the Protestant polities in Germany, but not would it be completely defeated.

It guaranteed, in theory, though of course not for long in practice, that the various kingdoms, republics, empires, states etc. of Europe would be sovereign on an equal basis within their borders.

TL:DR: While it understandably often gets mixed up with the contemporaneous process of state formation, this isn't the primary reason that the Treaty of Westphalia is sometimes framed as marking the start of the era of modern sovereign nation states. Rather, it's because it asserted the sovereignty of Europe's smaller polities in the face of supranational ambitions such as Catholic church, Hapsburg Empire, French monarchy, and the concept of pan-European Protestant revolution.