Depends on the aspect. In terms of a higher level of thinking/problem solving/philosophy and the ability to craft tools and innovate, absolutely.
However I firmly believe that animals have humans beat on a few things; physical abilities, body design, and morality.
Physically they tend to be faster, more agile or have a much higher level of strength. Their physical abilities are much better adapt for survival and/or hunting than humans'.
On the same plain, they tend to have less flawed bodies. In the sense that the human body can be unstable. I'm talking things like, biting your own tongue is possible due to the structure of the mouth. Spines are literally pretty weak. And, most famously, the male reproductive organ (aka a really sensitive point) is exposed and ill-protected. Other examples;
link Animals don't seem to share these issues.
And finally, despite the human ability to reason and use logic. Despite the ability to empathize, humans are senselessly violent. Sometimes you can see that in animals but usually their violence serves a purpose; survival. They kill only to eat or to secure their bloodlines via mating rituals. Humans are (as far as I know) the one of the only species that kill for sport or vengeance.
That said, humans also have the ability to be more compassionate in a way that some animals aren't. Humans can show affection in different and creative ways and can empathize and sympathize in more complex manners. They can express compassion in more elaborate ways.