A lot of nonsense is written on this rivalry by both Italian and Chinese authors, and even more spoken in conversation. Quite often this nonsense is stimulated by national pride, and alcohol.
From National Geographic News online 28 Oct 2010
The origin of noodles and pasta is ambiguous. In 2002, noodles claimed to be 4,000 years old were discovered by Chinese archeologists in Lajia, an archeological site in the northwestern province of Qinghai. The find was given credibility by its publication in the scientific journal Nature in 2005. These noodles were made of two kinds of millet, known as foxtail and broomcorn. They looked good in the photos which were circulated.
A serious difficulty with this widely reported find - from BBC News to National Geographic and many newspapers all over the world - emerged in several later articles. It was shown, for example, that while the authors of the Nature article specified that the ancient noodles were “pulled” just as they are today, in fact that technique - which we see in the whirling noodle demonstrations in Shaanxi and Shanxi just as in the pizzerie of Naples - is impossible with noodles made of millet since that grain lacks the gluten which provides the necessary elasticity for such displays.
Let’s consider the historical record.
In fact the grinding of wheat or rye and subsequent mixing with water was carried out in both Europe and Asia in neolithic times. But that didn’t make noodles or pasta. In China, the earliest written record of noodles is supposedly found in a book dated to the Eastern Han period, and noodles made of wheat flour did become a staple food of Han people during that time. In Italy, around the time of Christ the Roman poet Horace (whose real name was Quintus Horatius Flaccus) mentioned fried sheets of dough which he called lagana, a word which is still used today of a kind of unleavened bread in Greece and is probably the origin of the modern Italian lasagne. A little later the Greek author of medical texts Galen (Aelius Galenus) gave the name itrion (in Latin itrium) to any mixture of flour and water. Medieval Arabic authors used the form itriyya of dried forms of pasta boiled in water, and wrote that this product was imported from Sicily - which the Arabs ruled for around three hundred years.
Now the most obvious thing here is the striking temporal parallel between Chinese and Italian evidence: the beginning of the period known as Eastern Han, in 25 AD when the Han dynasty moved its capital from Xi’an eastwards to Luoyang, corresponds closely to the lifetime of Horace, who died just thirty-three years earlier in 8 BC. In view of the link with Galen, who was born in 129 AD, it is worth noting that Horace’s birthplace in southern Italy, Venosa, was said to have been founded by the Greek mythoogical hero Diomedes and lay on the Via Appia - which was the ancient road from Rome to Brindisi, whence ships sailed to Greece.
The application of Occam’s razor would point to more or less simultaneous origins for noodles and pasta, which was in fact the case of most “discoveries” and “inventions” from the neolithic period through to historical times.