3 red lights aside, MS with 360 was great, really good planning and execution. If wasn't for Nintendo fairy tale they would win that generation.
To be honest, if Sony hadn't messed up they would prbably have won that generation not Xbox (or Nintendo).
Wii did amazing but had a short life and hit approx 100 million. It also didn't really compete much demographically with 360. I doubt synth much would have changed Wii performance and certainly it was untouched by PS3 and 360 through out its life. It was its own thing in its own market.
MS got 360 "right" but initial sales weren't amazing and the market was clearly waiting for PS3 after PS2 and all Sony had to do was deliver what market wanted to outsell 360.
Then when PS3 hit it was way top expensive for many because at the time it was basically a console and blu ray player combo vs much cheaper DVD option. Crucially it also had shit PSN vs well established Live and it was also a bitch to code for meaning initially games simply performed better on 360 (first year or so it was literally 60fos 360 version vs 30fps PS3 version IIRC).
That combo allowed market to see 360 as actually better option for current trends (online and shooter/action titles) and thus we got more or less a tie when Sony managed to pull of some 180s of its own and leverage its bigger brand and global market.
Had Sony got PS3 right I'm pretty sure it would have outsold Wii WW while 360 would have still been a success but less dominant in US dropping its total sales a bit WW. Ultimate I would have expected a result, if all three made all right choices, of a close result with PS3 first, Wii close behind and 360 not too far behind that. WW that is, I think US would have still seen 360 ahead but by much less of a gap.
It's all "maybe" but if you look at all three last gen and what they got right/wrong and the sales profiles of each market it's obvious Sony essentially "lost" the gen via a string of bad decisions coupled with good decisions from MS and Nintendo (well TBH Nintendo made risky decisions that struck gold which is their bigger issue overall only MS seemed to execute in a knowing way for Western market and US in particular at that time).
TBH it's the core brand and market Sony has that convinces me they need to screw up before competitors can top them (such as MS being way ahead with online for a period). That they could win 3 out of 4 gens and be more or less a draw for second place despite awful market blunders indicates they are tough to dislodge. It's hard to say why but the market performance speaks for itself. Nintendo are all over the place. I love 'em and they take crazy risks but as a business they are now unreliable in the market. The risk pas off and you get Wii, the risk doesn't and you get Wii U.
MS are solid but they seem to have X core issues:
They simply cannot get enough traction globally it seems. Without a stronger WW performance than even 360 they're never going to win a gen IMHO
Live/online aside they're too reactive and don't take enough risks. They follow a bit too much leaving themselves open to being caught off guard. They also cling too much to core IP
They try to push their strategy to consumers too much beyond pure gaming (XB1 being worst offender). They need to commit to gaming market first and foremost if they're going to have a console and extend logically from there. Trying to push a half console half new form of media consumption/interaction market didn't want dent work. Sony had same issue using PS3 to push blu ray ahead of market demand.
Thus far for Sony it seems just providing a solid console is the way to go coupled with regular new IP and not missing core trends like online gaming. The PS3 is their worst hour and it combines pushing their market strategy ahead of consumers with being late to a key trend (online gaming) as well as ignoring preferences of developer community.