Two sentence have the same meaning.The only difference is that “我的眼睛大” is more formal while "我眼睛大“ is less formal.In oral language,Chinese people usually omit the possessive symbol “的”.
And we usually make the whole phrase consistent.For example,we say "我国” or “我的国家",but we hardly say "我的国””我国家”.Because “国“ is is less formal and "国家" is more formal.
Hope it helps.