In all fairness, the Ottoman Empire was still on-par with European Great Powers such as Russia and Austria until the latter part of the 18th century. It's only after the Ottoman Empire completely missed out on the reforms that came with the Seven Years War that the Ottoman Empire really started to lose the ability to compete as a peer with European states. And throughout the 19th and early 20th centuries, the Ottoman Empire was able to give a better account of itself vis-a-vis European states than most other non-European states, Japan being the only real exception.
The Islamic world could have been more "competitive" had Islamic states remained stronger in the 18th century, a time which saw consolidation and growth of state power in many parts of the world such as China, Southeast Asia and of course, Europe, but which in the Islamic world saw a near-century of division and infighting in Persia, the collapse of the Mughal Empire, and the weakening of the internal structure of the Ottoman Empire. Hell, keep the Mughals healthy and you can butterfly the British Raj, which won't stop European industrialization, but will take away the linchpin of European power in Asia.
Industrialization guarantees a European economic edge, and the chances of replicating that elsewhere were pretty slim, at least if Kenneth Pomeranz is to be believed. But this economic edge doesn't last forever. Japan, South Korea and now China utilized their positions to develop manufacturing sectors that are the envy of countries such as Britain. Part of the problem is that while East Asia has had, very broadly speaking, some good times from about 1950-1980 (depending on the country you're in) onward, much of the Muslim world has instead experienced economic stagnation. Tempting as it may be to look for the causes in Islam itself, the truth is that Muslim countries from Morocco to Indonesia have a whole host of different conditions that have resulted in this stagnation, and though the Arabian Gulf is rich because of oil, just having oil on its own is no guarantee of wealth (look at Libya, Venezuala, etc...).
A lot of rambling here, but if you're looking for an Islamic world that is competitive, it's actually fairly easy and there are a number of different ways you can do it. As for an Islamic world that is dominant, well that's harder. My instinctive answer is that an Islamic world that manages to unify the Mediterranean Basin might be the best option. If Muslims can seize places such as the South of France and Italy, as well as the rest of the Eastern Roman Empire during its initial wave of expansion, Northern Europe will be far more severely isolated than it was in OTL for longer. Hell, there's no telling what will happen in the long term.
This however is a bit of a wankish scenario, and while far from impossible, isn't exactly very likely either. It requires quite a number of things to go differently for the Muslims in several different areas. The idea of the Mediterranean being unified under "Dar al-Islam" allows for a greater growth of trade and for the Mediterranean to take on the same kind of role that it did for the Romans, rather than being the home of Muslim and Christian Corsairs for centuries, retarding growth and making things generally "a bit shit".