It totally depend on your data, which you want to store.
SharedPreferences
1) Small data.
2) Unstructured.
3) Like login info, user prefs, etc.
SharedPreferences is a key/value store where you can save a data under
certain key. To read the data from the store you have to know the key
of the data. This makes reading the data very easy. But as easy as it
is to store a small amount of data as difficult it is to store and
read large structured data as you need to define key for every single
data, furthermore you cannot really search within the data except you
have a certain concept for naming the keys.
SQLite
1) Large data.
2) Structured.
3) Organized.
Large amounts of same structured data should be stored in a SQLite
database as databases are designed for this kind of data. As the data
is structured and managed by the database, it can be queried to get a
sub set of the data which matches certain criteria using a query
language like SQL. This makes it possible to search in the data. Of
course managing and searching large sets of data influences the
performance so reading data from a database can be slower than reading
data from SharedPreferences.