Kwonger Class of 2014 here, so my info may be outdated. (Note 1: From memory, the Monash Scholars Program started with Class of 2015, so KLDYS was my only option out of the two unis. Note 2: I ended up going to Monash for uni mostly due to convenience.)
It gives u credibility, they only accept 1 person per school
Pretty sure that KLDYS accepted more than 1 person/ school. At least, this was true for my own cohort and for a number of years after, as I've heard from others. In fact, depending on how far your school is, they often accepted 2-3 students a year from a number of metropolitan Melbourne schools. Monash Scholars program had more of a record of having 1-2 students/ school, if I recall correctly, being the "younger" program.
Pre-COVID, both the KLDYS and Monash Scholars Program had a lot of networking events with discussions on future pathways and careers (probably the biggest calling card were the events). I remember doing a mock legal debate at UoM for students interested in law, getting free lunches (let's just say that I had a penchant for their brownies) and attending VCE revision lectures for some of the 'bigger', more popular subjects e.g. Methods. I certainly met and talked to a lot of people, which helped pull me out of my shell a little (I used to be very shy pre-Year 10).
To be honest, I never ended up using the library since it was a fair distance from home, but I'm sure it was helpful to others who got the chance.
I just got accepted to the Monash Scholars Program (yay!!) and I was wondering if it was still worth trying out for the Kwong Lee Dow Program (the applications open up in August).
To answer this original question though, either way, you're in a good position. Both programs are great in their own right.
Does anyone have any words of advice for me and do you think it is worth applying for the KLD program as well?
My own advice is to highlight your leadership experience during your application, and if you lack it, then whatever community-related extracurriculars you have. Since you already got into the Monash Scholars Program though, you likely already know this.