My colleague has built two of such antennas (unfortunately non-planar), for 900 and 1800MHz (used as detector of mobile phones in a jail!).
He successfuly designed it in IE3D full-wave MoM simulator. I'll ask him for details if you want.
Regards,
Eirp
Moreover, as I heard from some antenna design, the planar inverted-F has a broaden bandwidth, so how can we control the planar area and where we place the feeding point because it is not so single like a L-antenna? It is now three-dimensional structure.
You may like to check the book broadband compact antenna or the paper by BL Ooi on broadband stack antenna which has far superior performance with inverted F-antenna.
The main differences are:
1) Easy of construction, the PIFA is easier
2) Influence of ground planes around it, the PIFA is more susceptible to it,
specially for impedance.
3) Bandwidth, the non-planar has greater bandwidth.
4) PIFA is easier to match, since you can have a CPW transmission line
and use L/C network for matching