YouTube has not gotten worse. That's ridiculous. The quality was absurdly low pre Google. Worse than default 240P quality now by a wide margin, and Flash only. Google already had Google Video and the two co-existed for a while. It was bad quality too but as a brand YouTube had a hook and more people were using it.
VIMEO is generally higher quality on average but they have a lower ceiling on quality and highly restrictive limits on content. VEOH and other sites that want you using some janky proprietary player or non-standard codec are out of the question.
Google made YouTube ubiquitous and available, not entirely transparently, across all major platforms and various STB and other proprietary devices (that need to arrive at some unifying standard). YouTube pre-Google may or may not have been able to position themselves to do such a thing.
What hasn't been good since Google took over is their UI has only become more convoluted. Anything that requires more than one screen, more than one menu interface, etc. and Google doesn't know what to do. Google doesn't know how to present all that it offers, beyond search, in a logical intuitive way and this handicap has made its way to YouTube. They were good with one box to type words into and hit search and that's about it. Anything else that isn't a mess to use, however useful it may be, they acquired.
Google couldn't create something like Android themselves, not a chance. But they gave it a fighting chance in the marketplace and, like YouTube, it's now dominant. Moreso than an even messier, less sophisticated company like Yahoo.