From what I can see, enhanced E4 outperforms the therm-app significantly!
mjlortons video seems to have a ~3 degree temp delta, whereas the image by Bud has a ~8 degree temp delta.
Same with the handprint, jeffB's image has a 8 degree (celcius) delta whereas mjlortons video shows a 2 degree delta.
Here's a comparison using very small temperature deltas.
Therm-App:
Noise and resolution test
FLIR Hacked E4, Hacked E40, FLIR One (G1):
a sensitivity test
Flir E40 (hacked 320x240), Germanium (?) lens
Flir E4 (hacked 320x240), Chalcogenide Glass lens
Flir One => Lens FOL 2 (80x60)
As you can see at low temperature deltas the Therm-App does much better than the hacked E4 and is near the hacked E40.
Still not the same target temperatures though (only the same delta), so still not a super accurate comparison.
Please note that I used the Therm-App and the included lens (with f/1.1 aperture), whereas mjlorton used the Therm-App TH and it's included lens (with f/1.4 aperture, much darker).