I have a few questions for you, is there more of an independent aspect to honours? Does the place that you do your honours really change your experience? Finally, is there any place that I should preference?
The thesis will be the independent part of honours, no doubt about it. You will have a supervisor or supervision team to help you out, but it's pretty much up to you to own that thesis from start to end. I met with my supervision team to specifically discuss my thesis once every two weeks, but it differs depending on the supervisor(s).
The only thing I can think of that would change the honours experience between unis is staffing and equipment. Certain unis may have access to particular researchers/experts (which are part of the supervision pool) or specialised equipment that allow for a wider range of possible research projects. I genuinely think the overall honours experience would be similar between unis though.
I can't really tell you to prefer one uni over another as I never applied to any other honours program outside of Monash. I assume you're doing the Monash BPsych which comes with the reduced entry requirement. I went through the Monash BArts which had a higher requirement, and I believe the standards for non-Monash students are even higher. Consider the basic things such as travel time, entrance requirements, etc. I'm not too well versed on how entrance requirements change at other universities when you're not already a student there, but it's something you should consider if you don't want to continue your honours studies at Monash.