"Bigger" can be a vague term and there's a lot of disagreement over what it truly means. Some refer to profits, others revenue, others marketshare, active install base, etc.
If you're referring to profit or revenue, then Xbox is bigger no question.
If you're talking about marketshare, then your question almost impossible to answer. The Xbox leads in the US and UK by fairly large margins while the PS3 leads in Japan by a huge margin along with moderate leads in essentially the rest of the world. Globally, the difference is tiny and I don't think we can precisely say who has more consoles in homes. The difference between the PS3's sales and X360's global sales is so minuscule that a factor like defective consoles (which I think most agree was more problematic with the 360 than the PS3) could shift the lead in the PS3's favor. In any case, whoever the true 'leader' is, it probably has a negligible lead.
Even though no console has a considerably larger marketshare than the other, I'd say the X360 does have the larger active install base, or at least it has more active users. The is because the areas where the Xbox 360 does have a hefty lead (US and UK) are also the most active areas in gaming, which leads to the X360 usually experiencing more retail software sales. However, that trend is starting to change as the gap between the PS3's and X360's software sales shrinks year after year. Then again, there's still digital sales which I can only assume the X360 is leading in due to being larger in markets that spend more on gaming.
It's also worth mentioning that the PS3 has been outselling the X360 since it launched, mostly since 2009 . Make of that what you will though. The PS3 vs 360 difference last year probably falls within VGChart'z margin of error I think. It's all very closse.