Engineering is not such a black and white field. There are many roles in the engineering sector and the biggest advice I can give you is to ask lots of questions of people in industry and find out which role you would like.
The field is made up largely of both technical and managerial work. There are many different kinds of technical work and many different kinds of managerial work. I'll create an example scenario to help paint the picture, I'll avoid technical terminology and it's all completely fictional to help you out.
An engineer at Boeing has learnt that due to climate change, there is an increase in the amount of acidic chemicals in the atmosphere meaning that the plane wings are starting to corrode. This in itself requires a huge team. It requires a team of materials engineers to find a profitable solution, chemical engineers to look at the chemical composition of the sky, structural engineers.
John is tasked with, 'find a new paint to coat the plane wing that will stop corrosion.' Imran's job is to test the adhesiveness of the paint under high-velocity and whether there is a danger it will come unstuck. Tom's job is to interpret the data that John finds and work out whether it is affordable to the company. Desmond's job is to manage the team searching for a new paint.
John does technical work. He is an example of an engineering professional, he will need investigative methods and novel design to a problem that hasn't been seen before. This work is generally difficult. An example of his career might be that after graduation, he went directly into industry and has been solving technical problems all his life.
Imran is also doing technical work. Imran is also an engineering professional. Imran's career was different, he finished uni and went into industry. He realised that it was cost-ineffective to replace the material of whole wings and did a PhD in methods of advancing adhesiveness in high-velocity structures at uni. His knowledge is very rare and very applicable. most importantly, it is profitable to this firm. His work is highly paid.
Tom's job is an example of an engineering technician. Tom isn't as good as what he does as his two counterparts, so he gets smaller tasks. He graduated from uni and his skills, for whatever reason, weren't of the level to be performing highly complex tasks and so he takes slightly smaller tasks.
Desmond is the manager. This is not technical work. Desmond probably is paid more but he's charged with getting the most of his team. Desmond would delegate the tasks and it's an easy job when all runs smoothly. However, if Imran isn't able to do his job, he needs to bring someone in or get it done himself. Managerial work can be easy and it can be very hard.
These are all different roles and you need to think about where you want to end up and start asking people how you end up there. There are maybe 10-15 different general types of roles like this in an engineering firm. High-level managers, low-level managers, engineering professionals, engineering contractors, engineering technicians, technicians and loads more.
If money is purely your consideration. Then just get really good at one of those roles, it honestly doesn't matter which one. You need to have a set of skills that can make a firm a lot of money, if you can do that, you will be heavily compensated. If you don't, then you won't be getting paid the big figures.
A technician can make as much as a manager. If you're the only plumber who knows how to fix bolted doors with Aluminium corrosion and a chemical plant needs that to stay operations, you're worth loads. If you're an excellent manager whose team consistently runs smoothly and is highly profitable, again, you'll make loads.
With respect to the Melbourne v Monash debate. Melbourne's masters degree is a masters degree. You learn a lot of advanced methods and the masters subjects are harder and more is expected of you than undegraduate studies. Does it help? That's for you to say really. If you're getting something out of it that you think will make you more profitable to a company, then it's a good idea. If you don't feel you have skills to gain from a masters, it won't help you.
Ignore the naming differences. BEng(Hons) and Masters of Eng are just marketing ploys. Melbourne's degree is an extra-year of education, masters level education.
Also, it should be noted, a BSc and a B.Eng is not the same thing. Scientific method and engineering method are not the same thing and only a layman would put them down as interchangeable. I think that if you do your BSc properly, that is, you choose units that are meaningful throughout, you will have both an appreciation for scientific inquisition as well as engineering principles. Obviously if you choose the easiest breadths throughout and do overly-easy elective units that you cram for you don't see this, though.