What's the difference with my 9V battery and his 9V battery?
The difference is the chemistry of your "Extra Long Life" (Zinc-Carbon or more likely Zinc Chloride) 9V battery vs. video battery.
Not sure what is inside your 9V battery. What is known is your "Extra Long Life" has less energy capacity than alkaline. You would need to look at an zinc-carbon or zinc chloride datasheet to see the discharge characteristics.
This is only a 50 mA discharge curve for 9V batteries.
Why are 6xAA batteries (1.5V) recommended over a 9V battery?
This is not totally correct. One might say use AA alkaline rather than AAA or AAAA alkaline. Or use alkaline rather than zinc carbon. I suspect that 6 AA may still be better choice than 6 AAAA or 9v alkaline.
There are 6 AAAA alkaline batteries inside a 9V alkaline battery.
This is a 9V Energizer alkaline battery.
Source: 9 Volt Battery Hack!
The zinc chloride cell is an improvement on the original zinc–carbon cell, using purer chemicals and giving a longer service life and steadier voltage output as it is used. These cells are usually marketed as heavy-duty, extra-heavy-duty, or even super-heavy-duty batteries, and offer about twice the service life of general purpose zinc–carbon cells, or up to four times in continuous-use or high-drain applications.
Alkaline batteries offer up to eight times the battery life of zinc chloride batteries, especially in continuous-use or high-drain applications.
From Battery University.
Zinc-carbon, also known as carbon-zinc or the Leclanché battery, is one of the earliest and least expensive primary batteries. It delivers 1.5V and often come with consumer devices. The first zinc-carbon invented by Georges Leclanché in 1859 was wet.
Alkaline-manganese, also known as alkaline, is an improved version of the zinc-carbon battery and delivers 1.5V. Lewis Urry (1927–2004) invented alkaline in 1949 while working with the Eveready Battery Company laboratory in, Ohio, USA.
Alkaline delivers more energy at higher load currents than zinc-carbon. Furthermore, a regular household alkaline provides about 40 percent more energy than the average Li-ion but alkaline is not as strong as Li-ion on loading. Alkaline has very low self-discharge and does not leak electrolyte when depleted as the old zinc-carbon does, but it is not totally leak-proof.