It's always better to get a credit card issued in your name, rather than holding an add-on card if you wish to start building your credit score.
One important aspect of holding an add-on card is that if you fail to repay "your" dues on time even by a single day, the primary account holder will take a hit on their credit report.
I am not sure but I believe lenders (if they report additional cards) will report the add on cards to the account of the primary holder itself. So it may not help improve your score.
But if you want to get started with credit cards to get hold of it and experience how it works, then an add-on card will certainly help you get into that discipline.