HeatMan stubbornly clings to his ignorance:

Once they pex tubes are where they heat, they will be in
aluminum heat transfer plates stapled to the subfloor...

Sounds more expensive than warm air under the floor...

It is more expensive. But the comfort level is much higher.

If the floor temp's equal in each case, who would feel the difference???

....10 Btu/h-ft^2 might come from an 80 F floor with PEX and spreaders
beneath or an 80 F R1 floor with 90 F air beneath. An unfinished basement
ceiling might have warm air from a woodstove or gas heater under foil
or foil-faced foamboard stapled or screwed under the joists with some
holes in the foil to let air flow between the foil and the floor above.
The foil would lower the heat loss from the floor to the basement.

As an alternative, you might put 8' fin-tubes with 40 Btu/h-F of thermal
conductance between L' joists on 16" centers with (T-90)40 = Lx16/12x10
and water temp T = 90+L/3 F and cost C = $12/L per square foot of floor.
For instance, L = 24' makes T = 98 F and C = 50 cents/ft^2.

A basement with a suspended ceiling might have 8' fin-tubes below and
perpendicular to the joists on W' centers, with T = 90+2W = 98 F and
C = $2/W = 50 cents per square foot for W = 4'.

What's the cost of an equivalent PEX and heat spreader plate solution?

Floors are fairly good heat conductors. An 80 F R1 floor with an R1
airfilm resistance to 70 F room air above moves 10 Btu/h-ft^2, no?
So it only needs 90 F air beneath. Here's a diagram:

80 F
R1 | R1
T -----www-----*-----www----- 70 F

What's T? :-) 10 Btu/h--

Nick