Let's start with the terms so we're all speaking the same language. D-ILA stands for Direct Drive Image Light Amplifier, while DLP stands for Digital Light Processing. Aside from both acronyms starting with the same letter, there's not much else that's extremely similar about them.
DLP technology uses two key components to display a picture. Utilizing a light bulb as the light source, the light is reflected from a small DMD to the screen. The DMD is a Digital Micromirror Device and is roughly the size of a postage stamp. There is a minute little mirror on the DMD for every pixel of the display. These mirrors are hinged and either reflect light or not based on their position. This gets the light source to each individual pixel.
The only task left is to display the proper color for each lit pixel. DLP sets manage this through a color wheel that rotates several thousand times per minute. As the light is reflected from the DMD, it passes through the color wheel so that the right color is displayed.
D-ILA on the other hand, is a very different technology than DLP and is actually a variant of LCoS or Liquid Crystal on Silicon. Unlike DLP, D-ILA technology has no moving parts; so theoretically, there's less chance of a mechanical breakdown. You still have a light bulb or lamp as your picture source, but that's the essence of the similarities.
Comprised of three chips, D-ILA projects an image on to a silicon-based crystal display by creating the image on the chips. The light source is polarized by a Polarized Beam Splitter and reflects off of each of the chips. The image reflection is then focused through a lens, where it is magnified and projected onto the display, where there is virtually no space between pixels.
Both DLP and D-ILA are now capable of 1920 x 1080 resolutions. As far as which is better? Each has its advantages and disadvantages and ideally, the one that looks best to you is "best", so check both types of sets out.