Jail is almost always worse than prison. Prisons allow a substantial degree of freedom to lower and medium custody inmates, up to and including the ability to walk off the premises for work or education.
Jails do not have the resources and serve a very different function- jailers are preoccupied with handling writs, court functions, attorney/client meetings, visitations, a large and spread out number of intakes, discharges, first appearances, pulling inmates for questioning or new charges, and everything else. If you arent kept in a "dorm" or pod, you may leave your cell only for an hour or so a day. At the best you might get a trustee spot at a jail, where you can at least leave to go pick up trash or do maintenance around the property.
A prison has case managers, can transfer inmates to move them to more suitable programming or accommodations, and has more emphasis on training and education. Prisoners are encouraged to use their free time constructively, and the vast majority of prisoners have quite a bit of time that is somewhat unsupervised compared to in a jail, where they may wander the premises, sign up for coursework, read, write, or apply for work release or job placements. Most prisons aren't "locked down" outside of headcounts, sleeping times, or higher custody units.
My point is if you're stuck in jail prison isn't a threat... it's a bargaining chip.