What’s your former and latter database? Do you export and import data through any given procedure or do you write your SQL code yourself? Do you have binary data? Unicode-encoded data?
Save if you have binary data, exporting and importing should just be a matter of correctly re-writing the “CREATE TABLE” statements (because the datatypes and syntax may be different in both databases), the “INSERT INTO” statement syntax being pretty much universal among all RDBMSs. Of course, you may have to properly configure the TABLESPACE and all, but that’s a side task. The only point about which to be careful may be if you have Unicode-encoded data, in which case you have to pay attention the exported data is translated back into UTF-8 (and not the database native encoding for Unicode data), and to tell the database in which to import that the imported data is in UTF-8 (that may or may not be transparent, depending on your RDBMS).
For binary data, it would depend on if you have a direct access to the database data or not, so that you could export and import the raw data.