I assume from your OP that you want nothing comparable to WW1 either(and therefore no WW2)and no massive revolutions destroying Russia, the Ottomans and A-H. Such stability seems unlikely to me(primarily because no prior century has seen such stability, though I suppose their's always a first time). But assuming such a century long continuation of the Belle Epoque:
Austro-Hungarian Empire: The whole area is much better off economy-wise united. In part because of access to the sea and resources of individual regions of the empire and also greater security regarding internal and external threats.(sort of what NATO and EU are for modern Europe on a miniscale)
Russian Empire: Dubious. Was enjoying rapid growth which the war and revolution derailed, but the Stalin regime forced Russia's industrialization at the expense of rural areas- might not have happened without that force.
Ottoman Empire: Much like Austria-Hungary will benefit from unity resulting in stability and economic inter-access. The use of oil revenue will probably be less incompetent and the regime will probably be a first world one(Kuwait and Saudi Arabia already are, Iraq and Lebanon would be if it wasn't for instability, and modern Turkey is close. So it wouldn't take much to tip the empire as a whole over into the "first world" category).
British Empire: Without the drain of the 2 world wars it's global economic preeminence is extended, but probably wasted trying to hold it's colonial empire. This would leave the imperial territories in worse shape and possibly mean a crippled metropole economy then in OTL as well(trying to sustain occupation of +1/4 of the world's population for +50 years will do that to an economy). Unless of course they're smart regarding their empire and let it drift away.
French Empire:Much the same as Britain. But since it's metropole is more populous and it empire far less populous it would be less of a drain for them.
German Empire: Does it really need to be emphasized how much better off they would be?
United States: Short term they will be worse off without their displacing of Europe eased by the two WWs. But this also means they will be spared the Cold War and stay isolationist, sparing them the economic burden of the military industrial complex and easing progressive economics due to much less anti-socialist hysteria and the military not hogging funds.
China: Extended colonial era probably means they get fucked by Europeans and Japan. Might well be partitioned permanently, and in a weaker position economically today. The Middle East of our world that has been avoided due to a sustained Ottoman Empire is what this colonized and disembered China will resemble, except they won't have oil either.