In this country, the term platform bed usually means a plywood support surface. I much prefer slats for mattress support. Slats have some give and so act like wooden springs with each slat moving and flexing independently of the others. This makes for firmer support than a box spring, but one that is still flexible. Although individual slats may not look strong enough to support people without breaking, once weight is distributed across them, they hold up very well and their support is quite good.
Slats are a bit more work to make than a simple plywood platform.
They also will move around over time, leaving parts of the mattress unsupported, unless you provide some form of alignment or attachment. A plywood platform has its own advantages and disadvantages. Unlike the slats, the entire piece of plywood tends to sag as a unit. Sagging plywood is definitely not comfortable to sleep on because your spine will match the sag. However, a recessed box resting on the floor can easily support a platform on all bed sizes except the king.