Shulchan Aruch (O.C. 59:4):
וְלֹא יַעֲנֶה אָמֵן אַחַר סִיּוּם הַבּוֹחֵר בְּעַמּוֹ יִשְׂרָאֵל בְּאַהֲבָה, מִשּׁוּם דְּהָוֵי הֶפְסֵק
One should not answer amen after the conclusion of '...הַבּוֹחֵר'
because it is an interruption.
The Rema (61:3) disagrees:
רַק יֹאמַר אָמֵן אַחַר הַשְּׁלִיחַ צִבּוּר כְּשֶׁמְּסַיֵּם הַבְּרָכָה, וְכֵן נוֹהֲגִין, וְנָכוֹן הוּא
The Mishna Brurah (59 s.k. 24 and 25) explains that they are disagreeing about the nature of the bracha. The S.A. sees it as any other blessing that one makes on a mitzvah etc., so there cannot be a hefsek between this blessing and its subject, the Shema. The Rema sees it as different from all other blessings on mitzvos, as evidenced by the lack of structure standard to such blessings.
M.B. goes on to say that the general consensus of the achronim is in accordance with the Rema, but that there are those who nevertheless advise to finish with the shliach tzibbur, thereby eliminating the possible hefsek of an amen (one does not answer amen to a blessing he concludes together with the shliach tzibbur - see M.B. 51 s.k. 3 - otherwise one is generally obligated to answer amen to blessings - see S.A. 215:2).