Anyone in J on LATAM at LAX should seriously consider the Delta One lounge. LA J passengers are entitled to access on both departure and arrival and I found the experience to be excellent on our trip earlier this month. I had no issues getting access - the agents were very familiar with the rules. It is also not a particularly long walk between TBIT and T3.

I am not familiar with the Qantas offering so unfortunately I cannot provide a point of comparison.