library(dplyr)

df1 %>% inner_join(df2, by= "ID") %>%
  mutate(Count = coalesce(Count.x, Count.y)) %>%
  select(ID, Count)

#   ID Count
# 1 11   345
# 2 22   456
# 3 33   786
# 4 44   765
# 5 55   890
# 6 66   888
# 7 77   654