The sensors on both are the same from what I know.
I'm pretty much sure that's correct.
The 19mm lens has a smaller aperture which means it allow more infra red into the sensor. So the images do seem a bit clearer on the 19mm when there is very little temperature difference of high vs low temp. Like 1-2 degrees C.
I think you mean the 19mm lens has a
wider aperture so that it lets more IR radiation in. It's always confusing that a smaller number means a bigger hole for light to pass through!
The most sensitive lens commonly available for the Therm-App range is the 13mm f/1.0. It's the one I usually keep on my Therm-App and it is very noticeably better (less noisy) than the 6.8mm. The 13mm is slightly more sensitive than the 19mm, but not enough to notice in day to day use.
Here's a summary of the different lenses from Opgal:

and some sample images with the different lenses:


Overall, I find the 13mm lens the 'best' on a day-to-day basis. It's sensitive, has a decent field of view without being too wide or too telescope-like and is generally easy to use. The only downside is that it has a relatively narrow depth of focus, but this isn't a problem for imaging anything other than very close-up work or bigger items with significant depth.
If you're thinking of buying a Therm-App camera then I'd suggest you ask Opgal whether they'll supply it with the 13mm lens. It's not appropriate with the TH, which is calibrated for the 6.8mm, but the regular camera (or HZ, which I'd recommend if you can afford it) works
really well with the 13mm.
Do bear in mind (as has been alluded to earlier) that a thermal camera will not, generally speaking, give you a precise, absolute temperature of an object. They're pretty good at relative temperatures - this bit is hotter than that bit - but even a well calibrated camera may have an absolute uncertainty of a couple of kelvin. The Therm-App TH is no different from the others in this regard.
If your application requires simple spot temperature and min/max indication then I strongly suggest you investigate ThermApp Plus (on the Play Store, about $5) or ThermViewer. ThermApp Plus has very good manual controls, spot/max/min, and outputs in a variety of file formats including (I think) making a good stab at radiometric files. ThermViewer can output CSV files that record the temperature of each individual pixel as read off the sensor.