This gets my attention.
I generally enlarge my images via photoshop with their image size tool and it does a great job reprocessing images. (ALT+CTRL+I)
How does AIGigaPixel stackup with PS?
In some cases AIGigaPixel does an amazing job of (in the words of Topaz Labs advertising) "imagining" greater detail when it enlarges an image. This is not something Photoshop attempts to do. Adobe noticeably improved its enlargement capabilities in the last year or so but these improvements are more about retaining existing details faithfully. AIGigaPixel gives you three choices for its enhanced by artificial intelligence details ... High, Low and None. What I found with it so far ranges from amazement to disappointment. It just depends on the image.
I enlarged a one inch low quality image of a dog to six inches and then to twelve inches and it looked like an unmodified high quality photo. With each of two photos of people, I found an unacceptable hardening and loss of detail of the lips and mouth occurred.
I don't know if AIGigaPixel actually continues to learn and improve through use or if it simply is loaded with lots of possibilities. If it learns and improves, then amazement will grow and disappointment will shrink over time. But to answer your question, any comparison is apples to oranges. AIGigaPixel is intended to enhance details while Photoshop in intended to preserve them.