According to this badminton site:
Note that while all feather shuttles have actual cork for the “cork”
portion of the shuttle, some plastic shuttles use a firm foam “cork”
as the part of the shuttle that you actually hit. Know that these
materials have a great impact on how the shuttle plays and, if
possible, I would recommend that you stick with shuttles with actual
cork for the head. There are a number of plastic shuttle
manufacturers but the Yonex Mavis line seems to be the most
popular (though others from Carlton, Head, and Black Knight are
popular as well).
From Yonex USA site, the flight pattern of the Yonex Mavis 370 comes close to that of an actual feather shuttlecock:
From one Amazon review for the Yonex Mavis 2000:
This is a very good shuttle if you are looking for durability. The
flight is very near to a feather shuttle, but it falls just a bit
short because there is nothing like the weight distribution of a
feather shuttle from which you get better control and feel.
These links are all subjective, but all seem to indicate that nothing really matches the performance of an actual feather shuttlecock. Durability seems to be the largest advantage of the plastic versions. I hope this info will point you in the right direction for your search - please let us know which brand/model you decide on.