I think it's a genuine dilemma you've got there, and the decision you ultimately make will need to depend on what you personally want. I can't say I'm a law student myself, but I'm confident I can give you an informed opinion, especially since I've had personal contact with the inside of Melbourne's JD program. I have close friends who are Melbourne JD students, final cohort Melbourne LLB students, and I'm also acquainted with Monash LLB students. I'll try to make this as simple as possible.
Undergraduate (LLB) versus [Post]graduate (JD)
The Juris Doctor is a master's level degree, whereas the LLB is, of course, a bachelor's degree.
Each carries its own element of prestige; if you have a BA and JD, you can properly say that you "went to grad school", whereas a BA/LLB is a double degree into which entry is known as highly competitive. To be blunt, it's an largely artificial difference between someone who studied law when they were relatively older and more mature, and someone who studied law when they were relatively younger and still bright enough to stomach it all. And each has its flip-side, of course. To be even more blunt, there's a tendency amongst some LLBs to dismiss JDs as old people who for whatever reason "couldn't" do law when they were younger; and a converse tendency amongst some JDs to dismiss LLBs as younguns who found themselves in law without any real capacity to be passionate about justice and who are just driven and elitist.
Personally I feel that the University of Melbourne tends to market its JD along those lines I just mentioned, i.e. it's better to study law when you're older and supposedly more mature, having completed a bachelor's degree. They like to point out that the entry pathways attract people from diverse backgrounds, as opposed to a narrow intake of school-leavers with fabulous ATARs. And this is just me ranting, but I think it's rather ironic that, at the same time, Unimelb offers guaranteed CSPs to those with 99.90 ATARs, so long as they've completed a New Generation degree at Unimelb. It actually contradicts the whole Melbourne Model principle of "we want students who have excelled at tertiary level, not students who just aced their high school matriculation". Having said that, full respect to you; I'm not actually trying to make a point about who should or shouldn't study law (I only wish everyone who would and could study law had the opportunity); I just have a massive bugbear with the Melbourne Model.
Cohort difference
So then we come to the difference in cohort, which will affect your experience of law school. Generally speaking, you will likely meet a far broader range of personal backgrounds in the JD program, including a wider range of ages. And if you choose the Monash LLB, your cohort will be, almost without exception, other school-leavers like yourself who will have achieved excellent ATARs (congratulations, by the way!). So the question you need to ask yourself is, "Does diversity necessarily equate to disparity; does similarity necessarily equate to solidarity?" Remember: it's not so much a matter of which type of cohort would improve your performance at law school; just think about what appeals to you personally.
PS. If you've read the Melbourne JD promos, you will have got the wrap on smaller and therefore superior class sizes. But many proud LLBs would dispute the need for small class sizes in many if not most law subjects, and they would also point out that you don't need a university timetable to arrange you and your fellow law students into a study group-size group.
Degree length
Last time I checked, a BA/LLB took 5 years, while the New Generation Unimelb BA takes 3 and the JD takes between 2-and-a-bit and 3 years. The crucial point question is how much arts you want to study. When you do combined law, the time saving is made purely in the non-law degree, i.e. you only do two years worth of arts subjects, not three. So you have to ask yourself how important that extra year's worth of arts study is to you. An important thing to remember here is that the Unimelb New Generation degrees have various requirements that you complete non-arts subjects, and so the "density" of arts study is arguably lower than (1) what it was in the old Melbourne BA, and (2) what it is in the Monash BA. Both the Unimelb and Monash arts faculties have gone significant funding cuts and class size increases in the past five years or so (i.e. not just Unimelb; but personally I think Unimelb arts is in worse shape than Monash arts ... but then again one has to compare the two unis on a discipline-by-discipline (i.e. area of study-by-area of study) basis.
I have no idea whether you are limited to just one (as opposed to two) arts majors within the Monash BA/LLB program. I would rather let you check that thoroughly for yourself (if you haven't already done so), since the rules might differ per major, and I have no idea what the rules are on minors. I also don't know what exact the deal is with majors in the Melbourne BA (I'm a so-called Unimelb "heritage" student--a wanky name, I know; but what can one do).
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I could probably say more but I think you get the idea. My brother is in pretty much an identical situation to you and I've just given you the same advice that I gave him so you can be sure that I'm being as sincere as I can.
All the best with your decision and congrats again on finishing school!
