Since PM comes with Hertz Presidents Circle I get excited when I get to use Hertz for my gov’t travel but we’re always stuck using what’s cheapest. It’s more about hoping I can avoid certain companies when I can (such as Fox) rather than having a particular preferred company. For personal travel I’ll go with Hertz if the price is similar to other vendors so I can use the Presidents Circle and maybe get a sweet upgrade but otherwise I tend to go with what’s cheapest.
For hotels I’m often stuck on base but when I can get off base, it’s a toss up between Marriott or Hilton brands for me - generally whichever one has the closest property to where I want to stay that honors the USG per diem rate. I don’t have meaningful status with any hotel brand. If traveling with Mrs. ATOBTTR, we’ll go with Hilton since she does have status with Hilton and we can get the perks.