Problem with piezo readings and Arduino Due
The problem is timing.  When you tap or hit the sensor it produces an impulse response: a signal that increases to a peak, then decays back to zero.  You are expecting the code to capture the peak value.  Your code is spinning in loop() as quickly as possible, but captures just the first point above the threshold. The signal can still be increasing when you capture and print.

So imagine this stream of signal values

time  signal   analogRead()
      at pin   occurs
----  ------   --------
 1     190      190
 2     190
 3     199      
 4     210    
 5     220      220 - trips threshold, prints and then waits
 6     230
 7     260
 8     280
 9     320      (this point occurs during delay())
 10    280
 11    260


The same exact signal, but at a slightly different time could be read different by the code:

time  signal   analogRead()
      at pin   occurs
----  ------   --------
 1     190      
 2     190
 3     199      199
 4     210    
 5     220      
 6     230
 7     260      260
 8     280
 9     320      (closer, but still did not read the peak)
 10    280
 11    260


So the strategy of catching the first point above the threshold makes it unlikely you can capture the peak value.  There are two ways forward: hardware or software.

You could use electronics that latches the maximum value.  If you search "peak hold circuit" you will find many circuits that would capture and hold the peak.  That frees the Arduino to somewhat lazily spin in the loop and still be able to accurately capture the peak.  Once it sees the value is no long increasing, it resets the peak hold and goes back to waiting.

You could use code to capture the peak. Something along the lines of this psuedo code: 

lastreading = analogread()
if(lastreading &gt; threshold) {
  peakreading = lastreading
  keeplooking = true
  while(keeplooking) {
    nextreading = analogRead()
    if(nextreading &gt; lastreading) {
      // the signal is increasing, save this and see if next point is even higher
      peakreading = nextreading
      lastreading = nextreading
    }
    else {
      //signal is decreasing, the peak is over
      keeplooking = false
    }
  }


This software approach could still miss a sharp peak that occurs between analogRead()'s, but may be good enough for your use.