Petrof is a hand-crafted European piano made in the Czech Republic. Their history goes back to 1864. During the Cold War, they were part of a state-owned consortium, but after the fall of the Iron Curtain, they became privately held once again. They are one of the better European pianos, and certainly superior to anything the either Yamaha or Heintzman builds. Consequently, they are pricier.
Consider: Petrov hand-crafts some 6 to 8000 pianos per year. Yamaha produces 250,000 pianos a year in China -- their Japanese plant has been closed for virtually all piano production for over 4 years now, except for their concert grand, which they market at $130,000 US. All U.S. production has also ceased. I would not buy a new Yamaha these days -- I might consider a used one if it's not more than 20 years old. They tend to start out bright and get brighter over time, due to a rather high-tension scale, and a very hard hammer felt that does not take well to repeated voicing. At least that has been my experience with them. I also do not like overly-light actions, and Yamaha is known for that.
The Heinzman is a run-of-the-mill Chinese stencil piano. The name comes from a venerated and respected Canadian manufacturer now defunct. Today's pianos bear no resemblance to the genuine Heinzmans. They are an entry level piano at best. At worst, they are junk.
Cheers,
G.