For the most part, Boeing and Airbus don't produce equivalent airplanes because they aren't involved in regional jet business. The direct competitors include Bombardier CRJ900, Embraer E175-E2 or Mitsubishi MRJ90, according to Wikie[1]. However, with sale of CS 100 by Bombardier to Airbus as Airbus 220, competition is more direct, especially if future extensions of ARJ21 are realized. ARJ21 bears some resemblance to McDonnel Douglas MD-90, which China assembled under license last century, but they are not really in the same class, with MD-90 competing directly with B737.

A few things about Comac ARJ21 that make it unlikely that the aircraft will ever fly in the West. First, it is only certified by CAAC in China and there is no plan to try certification by FAA or EASA. Second, the aircraft is designed for hot climate and high altitude airports in Tibet. As a result, it is overweight and expensive to operate elsewhere. Third, there was a multi-year delay to certification, so the aircraft is now considered obsolete.

Although China owns IP rights to the aircraft design, engines and avionics are supplied by Western companies. Western parts suppliers had to shoulder more design work than normal for subcontractors. This aircraft is considered a learning experience for Comac, which is now designing C919, a competitor of B737 and A320; and C929, a wide-body aircraft in the same class as B787 and C330. Because of Western components, it is unlikely to be converted into military aircraft, which along with limited international sales means Comac will lose money with ARJ21.

1. https://en.wikipedia.org/wiki/Comac_ARJ21