If the Anti-Federalists "won" their points in the ratification debate and in the writing of the Constitution, the United States would have undoubtedly looked quite different. First of all, the individual states would have had their own powerful, individual legislature, executive, and judicial branches of government, "under the direction and controul of a supreme federal head for certain defined national purposes" (Roland, 2003: "Brutus": Essay #1). As a consequence, the states would have been able to impose their own taxes, duties, and excises and to go after those who failed to pay their debts to the states. In addition, the states would have had the power "of laying and collecting taxes, duties, imposts, and excises; of regulating trade, raising and supporting armies, organizing, arming, and disciplining the militia, instituting courts, and other general powers" (Roland, 2003: "Brutus": Essay #1). The judicial power of the states would have held precedence over an "inferior court that derived their authority from the United States" (Roland, 2003: "Brutus": Essay #1). Basically, while realizing the importance of having a well-established federal government, the states would have had many more powers and more of a say as to how their state was operated.
In addition, the individual states would have held more responsibility in matters pertaining to protection and defence of the community. For example, according to an Anti-federalist essay penned by "Brutus", protection and defence "ought to be left to the state governments to provide for the protection and defence of the citizen against the hand of private violence, and the wrongs done or attempted by individuals to each other-protection and defence against the murderer, the robber, the thief, the cheat, and the unjust person, is to be derived from the respective state governments" (Roland, 2003: "Brutus": Essay #7). This way the general government and the individual state governments would be held responsible for securing private and public justice, respectively.
Moreover, according to another Anti-Federalist essay penned by "Cato" on November 22, 1787, "[t]he most general objections to the first article [of the new government], are that biennial elections for representatives are a departure from the safe democratical principles-of annual ones--that the number of representatives are too few; that the appointment and principles of increase are unjust; that no attention has been paid to either the numbers or property in each state in forming the senate; that the mode in which they are appointed and their duration, will lead to the establishment of an aristocracy" (Roland, 2003: "Cato"). Therefore, the country would have had, like our textbook points out, "smaller electoral districts", more "frequent elections", and there also would be "a large unicameral legislature to provide for greater class and occupational representation" (O'Connor & Sabato, 2009, p. 54).
Finally, if the Anti-Federalists would have ultimately "won", the military would have consisted of "state militias rather than a national force" (O'Connor & Sabato, 2009, p. 55), which to be honest, could have caused many issues, such as raising the question of who would be ultimately liable for defending the nation as a whole against outside forces. In addition, these state militias would have further alienated each state from the next and thereby the nation would have been slowly pulled apart, which like what would happen less than 100 years later, the country could have been thrown into a civil war.
O'Connor, K. & Sabato, L.J. (2009). American government: Roots and reform (2009 ed.). Pearson Education, Inc.
Roland, J. (2003, December 20). Anti-Federalist Papers. EDSITEment.