Both of them are a slice-of-life kind of dramas. Age of youth focuses on 5 girls and college life, whereas Reply 1988 focuses on the children growing up (and experiencing their first love) as well as the family members. Both are slow paced, and detail orientated. It is definitely the smallest things that touch you the most. The music is also subtle and fitting. Characters in both shows have a lot of depth and show a lot of character growth.
Many life lessons to learn in both.
Overall the pace, genre, direction/cinematography (revealing details a bit at a time), music and feel of the two shows are similar.