Turkey’s vision for the Middle East is fundamentally different from Saudi Arabia’s.
Turkey dreams of replacing Middle Eastern dictatorships with pseudo-democratic, pseudo-Islamist, non-Sharia governments which, under Turkish leadership, can work together and advance to the point where they match the West in terms of strength and prosperity. Turkey is anti-status-quo.
The Saudi-UAE axis, on the other hand, is fully committed to crushing any democratic spark anywhere in the Arab world, in the fear that it will lead to a populist Islamist state that overturns the current Middle Eastern order that serves the Gulf monarchies very well. Saudi is pro-status-quo.
Disclaimer: This is just a quick, overly-simplified summary of the ideological rivalry between these two countries. Of course, each country is also constrained by geopolitics, domestic opinion, or economic limitations, and is sometimes forced to do things contrary to its ideology.