Do I have full control over the business?
Yes, as a sole trader you will have full control over the business.
If you are the sole director and only member (shareholder) of your company, then you will have full control over the company's management. However, certain decisions must still be recorded as resolutions of the company.
If there is more than one director, you will not have full control - the internal management of the company will be governed by all the directors and in accordance with certain rules, for example, the company's constitution or the replaceable rules.
Check out ASIC's Guide for Small Business Directors for more about your legal obligations as a company director.