Crawl space insulation in a humid climate is one of the areas where the standard approach and the approach that works have drifted apart. If you have fiberglass batts stapled between your floor joists and half of them are on the ground, you have seen the problem first-hand.
Why Floor Insulation Fails Here
Fiberglass batts installed between floor joists were the default for decades. In central Alabama they have a poor record for three reasons.
They absorb moisture. In a vented crawl space at Birmingham summer humidity, batts take on water, and wet fiberglass loses most of its insulating value while gaining a great deal of weight.
They fall down. Wire supports rust, staples pull out of damp wood, and the batt sags away from the subfloor. An air gap between insulation and the surface it is meant to insulate makes it close to useless.
They hide problems. A joist that is rotting or a pipe that is dripping behind a batt goes unnoticed for years.
The Approach That Suits This Climate
Insulate the foundation walls rather than the floor, as part of sealing the crawl space. Once the vents are closed and a vapor barrier is down, the crawl space is inside the building envelope, so the insulation belongs at the perimeter with the rest of the envelope.
Rigid foam board against the foundation walls, extending down and returning onto the floor liner, is the common approach. Closed-cell spray foam is an alternative, particularly at the rim joist where air sealing matters as much as R-value.
The rim joist deserves specific mention. It is often the single largest air leak in an older house, and sealing and insulating it produces a noticeable difference in comfort for a modest cost.
What You Should Expect to Feel
Floors that are not cold underfoot in January. Less temperature difference between rooms above the crawl space and the rest of the house. Reduced HVAC runtime, though the size of that saving depends heavily on the condition of your ductwork and how leaky the rest of the house is.
Anyone quoting you a precise percentage saving on your power bill before assessing your house is guessing.
Sequence Matters
Insulating a crawl space that is still wet traps moisture against timber and can accelerate decay. The order is drainage first if there is standing water, then vapor barrier and vent sealing, then insulation, then dehumidification. Insulation on its own, in a space that has not been dried and sealed, tends to repeat the fiberglass story with more expensive materials.