When comparing Knockout vs Polymer, the Slant community recommends Knockout for most people. In the question“What are the best client-side JavaScript MV* frameworks?” Knockout is ranked 2nd while Polymer is ranked 13th. The most important reason people chose Knockout is:
Knockout uses HTML5 data attributes to bind HTML elements to data objects in javascript. This allows more work to be done by the framework rather than requiring you to specify where data should be bound in the javascript. The data binding is very intuitive as the bindings are done within the HTML itself in the location it should be bound.
Specs
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Pros
Pro Easy data binding
Knockout uses HTML5 data attributes to bind HTML elements to data objects in javascript. This allows more work to be done by the framework rather than requiring you to specify where data should be bound in the javascript. The data binding is very intuitive as the bindings are done within the HTML itself in the location it should be bound.
Pro Easy to learn
Has a low entry barrier and an easy learning curve. It's especially easy to learn for beginners.
Pro Built in templating
Bindings in Knockout can also be used to control the generated structure of the HTML. There are bindings provided to allow for iteration and conditionals. The structure of the html reflects the structure of the data so iterative elements are bound to arrays in the data model. Having the HTML structure maintained by bindings keeps the templating simple, easy to read, and maintain.
Knockout also allows for string based templating so you can use whatever templating library you prefer.
Pro Legacy browser support
Supports a large number of browsers, including IE6.
Pro Great documentation
The excellent tutorials with built-in exercises are a great learning experience, even for people without prior MVVM and data binding experience.

Pro Lightweight and plays nicely with other libraries
Pro Dynamic models help with keeping the code simple and clean
Models in Knockout can be watched to keep the page data up to date by using observable objects. The observables notify Knockout when data is changed and automatically updates the page when this happens. By having Knockout maintain this relation, it keeps the front end code cleaner and simpler, and by enforcing a consistent pattern with observables the methodology can be more robust.
Pro Very flexible
One can do a lot of things and it keeps self references and other types of loops under control.
Pro It's only a library
Knockout does one thing, and does it well. It doesn't try to take on more than one area. It does MVVM data binding and that is it.
Pro Simple manageable modules
Using components is a great way of breaking up large modules into simpler ones.
Pro Various basic components
It provides a base component.
Pro HTML markup is not string
HTML markup as it can be a non-string.
Pro Flex layout components
It provides Flex layout components.
Pro CSS is easy to apply
CSS can be applied far more comfortably than React.
Pro No need for special debugging tools
The presence od specialized debugging tools are advertised by competitors. The all features of web components are natively supported by browser embedded development tools.
Pro Excellent routing
The router is embedded into CLI for project creation and covers as web as Progressive web app, also fused with Polymer layouts out of the box. The shop template for CLI has a complete solution including the routing.
Pro Complete web app stack support
Full app stack from data tier to routing, progressive web app, responsive layouts makes no need to seek outside of Polymer ecosystem for application features.
In addition to waste set of mature web components in Polymer Elements along with Vaadin Elements there are thousands of web components in the wild comparable to jQuery plugins set.
Pro Excellent documentation
Polymer guides you as with tools (cli, build environment, app templates,..) as with complimentary documentation on all phases of app development from creation of app as progresive web app to production deployment instructions.
As Polymer is standards based, the whole community around those standards also helping in documentation and support.
Pro Based on web components
Web Components are a collection of specifications released by W3C as a way to reduce the complexity of web apps by creating reusable components. Browser support is currently poor for web components, however Polymer is developed to make web components compatible with modern browsers.
Pro API is easy to understand, based on standard
The Polymer APIs are split on application layers and follow standards on all possible ways: Web Components, CSS variables, async API via Promises and so on.
Cons
Con Slower than others when amount of objects grows
Knockout has a bad performance when the dealing with large amount of objects. You can see more here.
Con Can become complex once the application grows large
Knockout leaves the application structure to the developer and it can become quite complex and unmanageable in the hands of a beginner once the application grows large and complex.
Con Two way binding requires a little extra work
When allowing users to edit existing data, the two-way binding of observables means you'll need to have to save original values before they're edited, to make comparisons or revert if the user cancels the action.
Con No server-side rendering
Polymer does not support server-side rendering. This results in higher loading times, more HTTP requests and it's not very SEO friendly, since search engines have no way of indexing a page if it's not rendered in the server.
