I am trying to create a few small animation sequences using JUST CSS3 or js, I do not wish to use both together. All I want to know from this is which one has more flexibility.
By flexibility I mean which one has more options for animation. I will be creating a webpage that has several parallax objects and the clients also wants a lot of animations on the page "fade in text", "slide in text", "bouncing error messages"
Which option is the best for the situation described above?
While I've always found animating with CSS a bit tedious, there's not that much you can do with vanilla javascript either.
If you expect to be handling a lot of animations, the best way would be to pick a javascript animation library to do the heavy lifting for you.
In your case I can recommend GSAP (https://greensock.com/) which comes with LOADS of features out of the box and is free to use in most cases (but still - do read the license before using it in a commercial project).
For an open-source alternative you can take a look at Velocity (http://julian.com/research/velocity/).
And finally, there's always jQuery for simple animations, but it often comes with performance problems, especially on mobile devices.