Is it better to lay Hardi Backer or Durock under 12"x24" porcelain tile ? And why.?

Hardibacker, with the joints offset and screwed every six inches on a full grid over the entire area.

That should prevent and slight movements cracking the joints above.

Before that, some extra [and long] screws through the plywood to the support timbers would not hurt.

Also use a high quality flexible tile adhesive, rated for porcelain tiles.

The tiles themselves should be near indestructible so any slight movement will show up at joints; the backing board helps stop movement being transferred to the tiles and joints.

If the floor that's there now, is moving because of soft dirt under the foundation, do not put any tile that large on the floor. A slight shift in the foundation again will cause some or many tiles and/or the grout to crack.

Also, is the floor itself rigid enough to support large ceramic or porcelain tile ?

If your floor has too much "bounce" to it, the same type of failure will happen.

The link below will tell you how to test if your floor is rigid enough for the tile job you want.

http://www.oneprojectcloser.com/tile-subfloor-thic...

Make sure your floor is flat before starting to tile. When prepping your floor for tile, trade your level for a long straight edge. Don’t be concerned with how level your floor is, be concerned with how flat it is.

Floor joists can heave or bow and by just looking or walking on the floor may not tell how un-flat it may be.

HardiBacker vs Durock ? Take your pick. They both do a good job. HardiBacker is a bit easier to work with.

And for the best results, also glue AND screw the chosen backer board down with a 1/4" trowel and thinset & the special cement board screws.

You may need additional plywood over what's down there now.

One more thing, use epoxy grout. It's more expensive and harder to work with, but it stays flexible when cured and does not need to be sealed as it is self sealing and does not hold stains in.

neither hardibacker or durock is rated for use over a single layer of plywood, plenty of people use it that way but the manufacturers don’t recommend it. you could be ok if its a light duty bathroom floor provided you do use mortar under the cement board but don’t do that in a heavy traffic area like the kitchen.

Ditra is the only underlayment I know of that the manufacturer recommends and warranties over a single layer 3/4 plywood