I haven't used HOD Preparing and/or Higher, but I've used SL for five cores with all kiddos. I just couldn't fathom doing two cores with them. It's just not in me. IF I let my eldest do all their work on their own, I could, but one of the things I most love about our homeschool is doing a unit of study together.
Now, we don't do everything together. They do their own math, vocab, writing, Spanish. BUT we do science together (Apologia) and history/reading. I don't want her to be doing her own thing without me being a part of her school life. KWIM? I know it works for many people. I'm not judging that. It's just a personal preference.
So... after using SL for Cores 3, 4, 5, 6, and 7 we switched to TOG. It was a lot of work deciding what books to buy for three levels (LG, UG and D). It as also really expensive. I'm a book junkie so trying to say no to books was next to impossible. Plus, my kids love to read and like to have plenty.
We went back to SL for this year, but that was always the plan. We are doing Core 5 for the second time. I absolutely love it and want each of my kids to go through it twice. IMHO, it's the easiest core to use with the whole family.
Note: for all SL cores, I spent extra money for extra books for my voracious readers and for the younger kids, to make doing the core with everyone possible. Amazon was my friend.
Honestly, I'm in the anxiety stage in deciding for next year. I hope you find a good plan for yourself. I might have been rambling too much. I hope it helps in some ways.