GA pilot reported an NMAC in the traffic pattern at an airport with a closed tower. The pilot of the second aircraft confronted the reporter after landing.

Narrative

ZZZ Tower closed; CTAF in use. I made callouts at 15 NM; 10 NM and 7 NM from airport announcing I would enter left downwind to land [Runway] XX ZZZ. Aircraft Y of unknown type announced south of the airport. Descended to approved traffic pattern altitude of 1400 msl; slowed to approximately 120 knots (24 knots below gear extension speed of 144 kts; and this is my typical traffic pattern entry airspeed) and was looking for the announced traffic. Approaching a store; which is a known local checkpoint southeast of the airport on the downwind leg; I asked on CTAF 'Aircraft Y approaching ZZZ Airport; what is your location reference the store?' A voice said 'LOOK UP.' I then saw Aircraft Y's lights above me and to my left at 9 o'clock; 400 feet above the pattern altitude (and therefore 400 feet above us). On CTAF I said 'OK; got you in sight; would you like us to make a 360 and follow you or do you want to follow us?' He said 'We will follow you.'I made standard left downwind; base and final callouts as recommended by the AIM (Aeronautical Information Manual).When the runway threshold was at a 45 degree position behind my left wing I commenced my base leg. The Aircraft Y pilot asked 'What type of aircraft is that?'; I replied. He replied 'Because you're flying a 737 traffic pattern.' I replied 'There's no reason for unprofessionalism on the frequency' and left it at that.After landing and while cleaning the airplane; the Aircraft Y pilot drove up to my hangar and berated me in front of my wife for 'screaming into the traffic pattern at too high an airspeed and being only 400 feet below him and they were talking to center with a Bravo clearance (wrong; ZZZ Tracon owns the Class B around here so he would be talking to Approach; not Center) and even the SIC (Second in Command) Center Controller didn't see you' and loads of other garbage up. You get the drift. ZZZ has lots of traffic and that's the reason I always approach the pattern at a way (for my airplane) slow airspeed; typically around 120 knots. I was making all the standard CTAF callouts and then some; and I entered the pattern at a known ground reference point.I'm filing in case he charges me with careless and reckless or anything else; which is absolutely not the case.