There are successful examples of both models when building out high-speed rail. The Japanese system often puts the new stations on the outskirts of cities and lets people do the last-mile transfer via the local metro system. Many cities have both a station with the city's name, which is in the urban center and serves the old line, and a station named Shin-Cityname ("New-Cityname"), which is on the urban periphery and serves the Shinkansen line. In other cities they do roll all the way to the old station (e.g. Tokyo Station), but switching onto low-speed track for the final connection.
Europe mainly decided to route trains through city centers, sometimes by also taking the strategy of using older, low-speed track for the urban portion of the trip, and accelerating to high-speed once the train switches onto the new tracks. However even there sometimes the outskirts option was taken when geography makes it more convenient; examples include Gare de Saint-Pierre-des-Corps (outside Tours, France) and Köln Messe/Deutz station (outside Cologne, Germany).
Europe mainly decided to route trains through city centers, sometimes by also taking the strategy of using older, low-speed track for the urban portion of the trip, and accelerating to high-speed once the train switches onto the new tracks. However even there sometimes the outskirts option was taken when geography makes it more convenient; examples include Gare de Saint-Pierre-des-Corps (outside Tours, France) and Köln Messe/Deutz station (outside Cologne, Germany).