The other thing to watch is this: are the two shapes strictly identical, i.e with the exact same number of decimals ?
When you query a geometry in Oracle with sqlplus, you will only see up to 10 characters (including sign and decimal separator), so you may not see all decimals. If you then do something like cut and paste the output to insert it into another table, you would be missing precision. Do
SQL> set numwidth 50
to see all decimals, then compare that to what you have on PostGIS.
Are the shapes in projected or geodetic coordinates ? Projected coordinates should show no or a very small difference.
For geodetic computations, differences in algorithms in the two platform may explain the difference you observe. I assume that you run both databases on the same platform ? Otherwise differences in math libraries, or in the floating point processing can also play a role. Note that Oracle uses the full description of the geodetic system (i.e. the ellipsoid and datum) for its calculations. I assume PostGIS does the same.