Kennedy was seen fairly universally as a president for change and for the hopes of young people. Whether correct or not, this meant that he would be seen fairly sympathetically everywhere. The Berlin Wall was about two years old in those days and after problems in Cuba and such, the status of West Berlin was seen to be far from comfortable. To have a US president expressing solidarity was a massive boost for the residents.

Domestically Reagan was from the right of the Republicans (neoliberalism) but that wasn't really the issue internationally. This article may give you a background on the politics of the time. Essentially, Reagan took a more aggressive stance towards the USSR particularly with regards to deployment of intermediate range weapons in Europe and then there was the Strategic Defense Initiative (also known as Starwars) which meant breaking the old ABM treaty, although in reality it wasn't formally killed off until the early 2000s. The problem is that the SDI gave the illusion of an America believing in a winnable nuclear war.

This was seen as sabre rattling and upset a lot of people, particularly in Social Democratic Berlin. However, Reagan was already making overtures to the USSR over intermediate range missile reduction and the famous speech "tear down this wall" was itself also an overture. There are arguments that taking such an aggressive stance was responsible for Gorbachev to withdraw support for the DDR but at the time, Many Germans saw this as war-like.

Edit: Qualified the "Germans saw this as warlike" as "Many Germans saw this as warlike". There were definitely those in Germany that were sympathetic to a hardened stance, but much less so young people.