Does Vampire Lestat have a lower budget than either season of Interview with the Vampire?

I've read somewhere around here that the reason Vampire Lestat is focused on the modern day rockstar faffing about instead of Lestat's backstory is because they didn't gave a budget for the historical sets.

Does that mean Vampire lestat has a lower budget than either season of the Interview? Because those managed to afford their sets. Did the execs give season 3 less money, or did the showrunners just blow what they had on songs?