I'm a MCDBA (so not an expert in Oracle but in MSSQL) but as a general knowledge I can say that it would not be fair to compare MYSQL with such a system like Oracle. MYSQL will be more than adequte for many things for personal data storage and since it's free it found itself a good niche in webservers but Oracle is a very powerful and proved stable db program. Buttom line is they are not in the same league and even MYSQL programmers admit that fact.
BTW if you are new to dbs, I wouldnt recommend starting it with Oracle. In fact I wouldnt recommend starting with any db programs. :classic: You'd better study SQL first, then you can go on exploring MYSQL. (which you can freely install to your local computer and work on it). If you have expertise in both switching to MSSQL or Oracle woudnt be too hard. My 2 cents..