This is really a subjective question. Every project using both technologies you describe will use different features from each, and it's impossible to make a blanket "this is the only right way to do this" kind of answer.
You shouldn't have to worry about them clashing if done correctly. Your bigger concern should be the additional and redundant work it may cause. For the large majority of situations, having Angular interact directly with WEB API is favorable because it eliminates a layer and makes your UI completely portable between technology stacks.
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The two can complement each other. MVC routing only kicks in when you make a server request. So long as no HTTP request to the server is made, then MVC routing doesn't kick in. I use the server for returning "dynamic content" that depends on some server resident information. You can fetch modals from the server as Partials. Using the Server for mostly API work is however advisable.
There is a project called TwitterBootStrapMVC (https://www.twitterbootstrapmvc.com/) That enables you to render pure bootstrap markup on the server and deliver it to angular after some "post processing". It is handy and works well with Angular.