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The GAI is a reasoning composite, that is supposed to be a "purer" measure of thinking and problem solving ability. The FSIQ includes other cognitive skills that are often important in learning, but are more closely associated with efficiency and output. On this instrument, those efficiency skills consist of working memory (represented by the picture memory score) and speed. The GAI is less-heavily weighted for memory and speed. So the moderately-sized difference between the FSIQ and GAI suggests that his actual thinking skills are better represented by the GAI, and that he may have less success with rote memory or attention tasks. Another critical point is that he is very young; small children can score poorly on tests for many reasons other than native ability, including fatigue, fluctuating attention, lack of familiarity with formal testing activities, or just their own idiosyncratic small child ways of interpreting instructions and situations.
So the lower picture memory and resulting FSIQ scores may or may not be "real", and if they are, may mean any one or combination of a number of things. But the GAI is definitely not a scam. It's a real thing, and often preferentially recommended as the composite score to be emphasized in GT decision-making.
I will also note that he did exceptionally well on a visual spatial task and an abstract reasoning task, which generally bodes well for his mathematical thinking. And yes, you should feel comfortable interpreting his results as indicating giftedness, especially in the non-language areas.
Whether one school or the other is the right placement for him is less-dependent on his numbers, and more dependent on the fit between his interests and finer-grained learning style, and the expectations of the school. Some so-called GT schools, IMO, expect excessive amounts of written work production (aka, busywork), which is best suited to children with high cognitive proficiency (efficiency skills) and advanced fine-motor than to deep, reflective thinkers. You will need to explore the temperaments of the respective schools a bit, and analyze how they fit with what you know of your child as a learner.
And, as many here can attest, keep in mind that your child's educational and placement needs may (likely will) change from year to year, so next year's perfect solution may be limited to next year.
