Interesting that gen 6 hit a peak at just year 3, and maybe this graph explains why gen 7 lasted so long as it was still selling extremely well (and no doubt making good money)
So comparing gen 6 to gen 7,
Gen 6 launched with the PS2 in 2000 (Year 1) and so out of the gate sales were high (although restricted by supply) and able to exceed 1 million that year. The next year saw PS2 sales rocket as well as the successful launches of the GameCube and Xbox which despite launching in the latter half of the year actually doubled the PS2's launch sales. So that's why year 2 is so high for Gen 6.
Year 3 for Gen 6 (2002) saw a price drop for the PS2 making it very attractive and again, sales increased dramatically. Xbox and GameCube sales were moderate. Whilst this is technically the peak year, sales in the next year (2003) didn't decrease that much thanks to continued PS2 demand and again moderately high sales of Xbox and GameCube which were now getting low in price (GC under $100).
2004 (year 5) again didn't see a huge decline as Xbox and Gamecube were doing ok and PS2 had lost some momentum but was clearly the market leader by far. With the launch of the slim PS2 and price cut to $149 we saw PS2 demand surge again end of 2004 and 2005 (year 6) but by this point the Xbox and Gamecube were dead. Hence why once again there is a small decline, then after 2005 the decline starts to become a bit more pronounced as it's pretty much just the PS2 selling but you can see how well it was doing just by itself and even outselling the PS3 in the USA till 2008. Gen 6 ended with an install base of more than 72 million in the USA.
Gen 7 started in 2005 (year 1) with the Xbox 360. Lets be honest here, at launch the 360 was nothing special, no one really bought one and the PS2 was still the console of choice. Hence why Year 1 is the lowest out of all gens. It was being sold at a loss as well and year 2 (2006) didn't fare any better for the 360 with fairly low sales again, 2006 saw the launch of the Wii and PS3 in the final two months of the year which gave it a boost but 2006 for gen 7 was nothing compared to what the PS2 sold in 2001 (year 2).
In year 3 for Gen 7 (2007) we saw the Wii take off and fly whilst the 360 was still doing ok and PS3 was doing terrible (off the back of PS2). This year aligned was the PS2's peak year and price drop year and so that's why Gen 7 year 3 just matched Gen 6 year 3. (Wii was supply constrained as well). Year 4 and Year 5 (2008 and 2009) saw the 360 maintain good sales, PS3 was still a bit meh but was gradually doing better whilst Wii was shooting through the roof and breaking all kinds of records. Especially when the Wii dropped the price in 2009 it gave gen 7 its biggest year yet thanks to that and increased 360 demand (HD consoles starting to sell).
With year 6 (2010) the Wii started to drop off but demand was now being fuelled by Kinect and PS Move and heavy promotion on these two HD consoles. (year 7) 2011 saw the PS3 and 360 peak thanks to the above again whilst Wii faded away almost. Hence why year 7 was the start of the decline. Of course year 8 was when sharp decline happened due to Wii selling nothing but the 360 remained strong along with moderate PS3 sales. Once PS4 was out there was huge demand after the long generation and so gen 7 sales dropped off a cliff.
So to sum up, Gen 6 started fast with the PS2 and saw extended sales over the years. Gen 7 started slow with the 360 and PS3 but the Wii broke all kinds of records, then the Wii faded whilst the 360 and PS3 picked up the slack and started doing the same numbers combined in later years.
Blimey that took some time to type out. Sorry for any mistakes.