I am moving and want to prevent as much stress as I can for my cats. They hate people, but the question I am struggling with is will they be less stressed in their regular home environment with our company while people pack our house, or less stressed being alone in a new, unfamiliar place? We are packing one day and traveling 1hr/ unpacking the next day.

PLAN 1: Close cats off in my bedroom at my current home with a 'do not disturb' sign while movers pack up the house all day. We will sleep at our current home with cats and then drive to the new house with cats and furniture in the morning. Cats will then be put in a bathroom while movers unload the truck. *downside is there will be a lot of people in their space making noise and changing things around while they pack and unpack.

... OR...

PLAN 2: Move cats to new house the day(evening time) before the movers come to pack. We sleep on the floor with cats in the new house. Humans leave in the morning to meet the movers to pack up the old house (all day project) while the cats are left alone, closed off in the new house. Humans return to new house at end of day and sleep on floor with cats. In the morning, humans return to old home and wrap up loose ends and travel back with the movers who will then unload. *downside is cats are alone in unfamiliar place and they still have to deal with people who unpack.

We're less concerned about what we have to do. We just want things to go smoothly for our kitties. Any advice or tips are welcome - Thank you :)

Is there a plan 3, they go to a cat spa, pampered for a couple of days, and you go get them and take them to knew home?

Definitely plan 1.
Many reasons, starting with being in familiar house rather than alone in unfamiliar place.
Movers don't always show up on time either.

I'd have to agree Plan 1 sounds like your best bet.
I've moved cats a few times and this is pretty much how I did it.
They will be a little stressed and unnerved either way.
But taking them over and then having to leave them will be too much for them.
What I always did also, was to leave the carriers open on the floor until they were ready to venture out on their own, I remember 1 cat in particular who stayed in his carrier for 3 days and only came out to eat, drink and use the litterbox, once he settled in he was fine.