Estonians are our northern neighbours (very good neighbours by the way) and in a way also rivals in healthy competition of two similar countries.
Tallinn Old City is better than that of Riga in two points - 1) it is located on limestone cliff - quite impressive; 2) Estonians have been wise enough and spared the Old City from the nightmare of modern arhitecture. They have construction boom nowadays, but - outside Old City. But Riga has some strong points as well.
Do I like Old Tallinn? Yes, I like it, almost as at home.