This depends on the particular era you're talking about. 700-1500 is a very long period of time. If we were to (hypothetically) throw a dart randomly on a timeline, chances are the answer to your question would be "yes" for whatever year we land on. If we're comparing a unified Chinese dynastic state to a single kingdom or state in Europe, the answer would be "overwhelmingly yes" for pretty much every single year between 700 and 1500. If we're comparing a Chinese dynasty to all of Europe, the answer is "probably."

I am going to largely ignore the Mongol era, because there is no question that the Mongol empire was the Eurasian hegemon during the short period in which it enjoyed political unity.

Given the political isolation of distant parts of the Eurasian continent, an analysis of global trade networks is probably the best metric for this kind of question. Beginning with Abu-Lughod (1989), historians including Chaudhuri (1990), Frank (1998) and Pomeranz (2002) have argued that the global economy from about 1000 to 1600 and even up to 1800 revolved around economic activity in Asia, including India but specifically China. Medieval Venice and Genoa, for example, derived their economic enterprise and success not from European production, but from their intermediary position along trade routes bringing expensive goods from India and China to European elites.

While the silver trade discussed by another poster here (EDIT: now removed) expanded after your proposed time period, it is also a useful framework for analyzing economic power. The fact that huge quantities of New World silver ended up in China (perhaps as much as half of all the silver mined in the New World) is less an indicator of Spain's economic reach and more an indicator of the kind of economic power Ming China commanded, and the huge global demand for Chinese goods. Chinese merchants accepted Spanish silver because it was the only thing Spain (and Europe as a whole) produced that had any real value in China. European goods were, to put it simply, too low-quality and too expensive to be competitive on the global market. Silver flowed from the Americas to China not because of Spanish push, but because of the incredible strength of Chinese pull. Spanish silver mining was driven by European desire for Chinese goods, not by a grand Spanish plan to construct a global silver-based economic network. Europeans were, to be quite frank, stumbling into a vast, preexisting Asian economic network and deploying their particular strengths (advanced oceangoing navigational techniques) to siphon off some of that wealth for themselves.

Pomeranz's (2002) main argument in The Great Divergence is that if we compare China, Japan, and coastal India to Europe along several everyday metrics (caloric intake, life expectancy, standards of living, wages, access to luxuries), then China, Japan, and coastal India remained on-par with Europe - and in some categories in certain places - exceeded Europe until 1800. Pomeranz's book has been the center of comparative world historical discussions since then, and I'm not sure I wholly buy his argument about the fortuitous location of coal deposits in Britain as the reason for the Industrial Revolution, but his quantitative arguments are difficult to dispute.

Another way you could make global comparisons is with population. Let's take the period smack in the middle of your proposed timespan: the 12th century (1100s), when the Song dynasty governed what was more or less "inner China." At the very height of the Song, just before the Jurchen invasion and the fall of the north, its population was 120 million. For comparison, the total population of all of Europe was around 60 million. A few centuries earlier, in the 800s, the Tang dynasty's population was probably around 80 million. I am not an expert on European historical demographics, and from what I know we don't have solid estimates for Europe's population before the beginning of the second millennium, but I have read figures ranging from 40 to 70 million. If we skip ahead to 1500, the Ming dynasty probably governed around 125 million people (a rough estimate given the breakdown of the Ming census process, but 125 million might even be too low), while Europe was probably home to around 90 or 100 million.

I know this answer is light on specifics, but I hope it gives you a broad answer. 700 years is a huge period of time and it would be difficult to break down numbers for each and every century.

Sources:
Chaffee and Twitchett, Cambridge History of China, Volume 5, Part 2: The Song Dynasty (2015)
Abu-Lughod, Before European Hegemony (1989)
Chaudhuri, Asia Before Europe (1990)
Frank, Re:Orient: Global Economy in the Asian Age (1998)
Pomeranz, The Great Divergence (2000)