Two same ADCs produce different result for same signal
I see a very large number of error sources in the data sheet.
 Some are mutually inclusive, some are not.
 There are 3 IC variants in the data sheet with different error levels and you do not say which you are using.  

You do not say what the input voltage is or what voltage reference you are using or if you have cross calibrated these devices in any way.
 Assuming 1V in pp and internal reference in own IC in each case then reference error is +/- 5 mV typical and +/- 35 mV worst case. 5 mV in 1V is 1:200 or about 1.2 bits in an 8 bit system or about 7 bits in a 14 bit system, and the worst case 35 mV is log_2(35/5)  ~= 3 bits worse again = 10 bits, so "only" 7 bits, before we look at  the other error sources seems "good" [tm].

It may be that you are sharing a reference (if not, do try it) or calibrating for reference or other errors or whatever, but if so you need to tell us.