Well, it's a little hard to say what was going on in Europe in the 1000s to 1300s, because they're a bunch of different countries. However, I would say that, broadly, life was not very secure for the average farmer, as your friend suggests. There were some periods of relative peace in some locations (particularly in the period from 1150-1300 or so), but if you were to look at, say, England over this time period, you'll see the last of the Viking invasions, the Norman conquest (and the Harrying of the North, which might have lead to ~100,000 deaths, about 5% of England's population), the Anarchy of Steven and Matilda, and two Baronial Wars. The history of England over this time period was not, I'd say, unusually violent by European Medieval European standards. Especially in the earlier part of this period, in the case of some areas like the Holy Roman Empire, stable governance was non-existent, and the problem was not so much that lords were unable to control banditry, as that it was hard to distinguish between bandits and lords.

On the other hand, China was not exactly the picture of peace and security that your friend suggests either. The Jurchens invaded and took over about half of the country in the early 12th century, and although they established a somewhat stable administration, the border between the Song (southern Chinese) and Jin (Sinicized Jurchen) dynasty was a quite violent place. Then came the Mongol invasion, which destroyed both the Jin and Song dynasties, and lead to vast numbers of Chinese deaths (from massacre, disruption of food distribution systems, etc) -- from census figured, death tolls on the order of 30 million have been estimated. (Note: some would argue that these deaths could have other causes, such as flooding in Yangtze river valley that lead to widespread crop destruction and famine independently of the Mongols, but this hardly suggests a particularly secure life for Chinese farmers either. A more optimistic interpretation is that the Mongols changed the census system in a manner so that millions of peasants just didn't count any more even though they still lived. This may be true, but I don't think there's any archaeological or documentary evidence that contradicts the overall picture that the Mongols caused death on a massive scale. )

So, both Europe and China were tough for the average farmer? Yes, but I'd say there were some differences.

In spite of all the war, when peace did reign, Chinese farmers throughout most of this period had less to fear from arbitrary, lawless government. China, whether under the Song, the Jin (Jurchens), or to some extent even the Yaun (Mongols), was governed through a system of imperial officials who were subordinate to the laws of the state. These officials could abuse their powers, of course, but at least the concept that there actions could be abuse existed. A European farmer was likely to be ruled by a lord whose authority was, in principle, based on personal privileges (e.g., whether he was granted high justice (power of life and death), or just middle or low justice), with no uniform system of accountability. So, one mark in favor of being a Chinese farmer.

On the other hand, the average European farmer -- at least Western European -- was materially wealthier and better nourished than the average Chinese farmer. This was most likely explained by the European pattern of delayed marriage, which resulted in fewer children per woman and more land for the average farmer to work. So, one mark in favor of being a European farmer.

On the whole, I don't know if you can say one or the other was better.