Companies can vary from engineering companies such as Honeywell or to big businesses like Dolby Digital, Energy Australia, etc.
It does depend on what field of engineering you go into though.
There's even the case where you could end up in a commerce firm or something.
The uni you attend is barely even considered. Its the marks you get and how those marks relate to the uni (so some unis have harder marking criteria's so a credit in one uni might be equivalent to a distinction in another). Also, your experience is the most valued thing (even more valued than your marks).
So yeah a wide diversity of companies take engineers and experience is a more valuable asset than anything else.