The differences of these two kinds of driving way lie on the way of signal transmitting, picture quality, the requirements for hardware.
Through the inset drive circuit, direct drive by TFT LCD transmits the photo signal to the TFT panel. Normally applied for TFT LCD of small size like mobile device or small display, the insert drive circuit is simple and demand lower requirements for hardware. But its performance on resolution,contrast and coloration is inferior to HDMI driving.
HDMI driving, as a kind of digital transmit, send picture signal of computer or other devices to TFT LCD through HDMI cable and transform signal into picture displaying on the panel by inserted encoder of panel. This way is used for panel of large size,such as television or surface display and it can provide support and provide with better picture quality and color performance.
But HDMI driving is critical about hardware,such as graphics card, CPU,memory.
AUO LCD:https://www.auo-lcd.com/products/auo-lcd-screen/
INNOLUX LCD:https://www.auo-lcd.com/products/innolux/