NHK ni Youkoso!, Koe no Katachi Recommendations
Both anime deal with the theme of suicide, as well as a male character being regretful of his hurtful actions towards a vulnerable female character.
Both are drama dealing with MC's incapability to connect with other people
Both feature various people from their pasts bearing importance for their character developments.
Koe no Katachi does have way more recent art techniques (and way bigger budget), while NHK ni Youkoso! is recognizably a decade older.
If you like the realism which characterize NHK ni Youkoso, you will probably enjoy Koe no Katachi. Both also tackle social problems such as suicide, bullying and isolation. Koe no Katachi is the first anime that satisfied me since I've watched NHK ni Youkoso.
As many have said before Welcome to the NHK is pretty similar to Koe no Katachi. Both of them deal with the issues of social anxiety, suicide and isolation. Although KnK is a bit lighter both of them are just as depressing.
If you liked Koe no Katachi you'll definitely like NHK.