from an earlier answer of mine

There were quite a few crossings of the inner-German border during the Cold War. One of the major reasons West Berlin was a major center for Republikflucht was that it was the safest alternative for a successful escape. The inner-German border was crossable in places through the 1950s, but it was increasingly becoming a military border as the Cold War formed. The GDR and the Soviets had already expelled some residents of the border for military reasons in the late 1940s and the area was heavily patrolled and armed as the Cold War escalated. Barbed wire, tank traps, and land mines became common features of the inner border starting in the 1950s. Navigating this area required a degree of local knowledge, timing (border troops sometimes deactivated the mines in winter lest snow trip them), and luck. The Wall's erection actually accelerated the process of arming and fortifying the inner German border. This somewhat staid and propagandistic US Army educational video from the 1970s illustrates how the border in its mature state was militarized and quite formidable.

West Berlin in contrast was a much safer area to make a dash for the FRG. The city was massive and had a large number of entry points for a would-be Republikflüchtige. Wartime agreements meant that the East ran the city's overground S-Bahn rail routes. A good many defectors simply bought a ticket and left at one of the West Berlin station stops. The SED tried to staunch this method of escape with MfS informers at rail stations and ticket booths, but it was too large of an area to effectively police. The Berlin's Mitte district fell under the Eastern zone, but it also had underground U-Bahn stations, which the Western zone ran in typical wartime agreement fashion. Other refugees simply walked across the border checkpoints from East to West Berlin. While such crossings were not without risks, there was considerable East-West foot traffic prior to the Wall. There were a not insignificant number of migrant workers who worked in the Western zone while residing in the GDR. A number of refugees also bluffed their way past border checkpoints claiming to visit family members or going on a brief holiday.

Although crossing the border with intent to flee became illegal in the 1950s for GDR citizens, it was very difficult for the SED to stop this outflow of people via West Berlin. The inner-German border may have been larger than West Berlin, but it was defended on both sides by two military blocs who had every interest in guarding this border. Berlin was a much safer alternative. A 1961 report by the MfS concluded that for every one individual stopped by the city's border and police controls, some six evaded these controls. West Berlin had become after 1953 the dominant egress point for a prospective Republikflucht; this graph (and it is a little pixelated) from the Federal Ministry of Refugees shows how Berlin, the red-shaded line, played an outsized role in the refugee crisis.