Again, you have to consider the protonation states of the ionizable groups on the molecule. At pH 7 and with no acetyl group, the amine will be protonated and bear a formal positive charge - this is a strong electron withdrawing feature, which you were right to consider originally. That positive charge won't be present with the n-acetyl group, so the thiol will be less able to ionize.
So, for cysteine vs cysteine methyl ester, what will be the overall charge of the molecule in each case with the deprotonated thiol? One of these is much more stable. Try drawing out both examples.