Well, you obviously have a Shield that is designed for a Mega2560 / Due. The clue is in the 18x2 header pins.
You have 2 resistor packs for the XPT2046.
And only 4 resistor packs for the microSD and TFT.
So you probably have an 8-bit parallel interface.
I suspect that your "other" shield has 7 resistor packs for the microSD and TFT.
Life would be so much simpler if you posted a link to your actual displays.
Since your shield says ili9488, I would think this should be a pretty big clue for the controller.
It is fairly unlikely that UTFT has got an 8-bit driver for an ILI9486 (or ILI9488).
The UTouch should work with any of these Shields. They all have an XPT2046 Touch Controller and all use the same Arduino pins.