What is the difference between @Inject vs constructor injection as normal parameter in Angular 2?

You really should only use @Inject for situations where the injectable token is not a class. If you are unfamiliar with what a token is, it is basically what Angular uses to recognize what to inject. For example

providers: [
  AuthService,
  { provide: Http, useValue: new CustomHttpImpl() }
]

Here we have two different providers, the AuthService and the CustomHttpImpl. With the AuthService the token is AuthService. This means that we inject AuthService, using obviously the AuthService type

constructor(private authService: AuthService) {}

With this constructor, Angular knows to look for the AuthService with the token AuthService.

In the second provider, we provide a CustomHttpImpl but this time we use the token Http. So we cannot inject CustomHttpImpl we need to inject Http, since that is the token

// this will actually be the CustomHttpImpl, not Angular's Http
constructor(private http: Http)

// error: No provider for CustomHttpImpl
constructor(private http: CustomHttpImpl)

So you can tell from this that the tokens are all classes, which is enough for Angular to figure out to how to inject.

But let's say we have a String, or an Array of something we want to inject. We can't tie that to any class token, so we need to create an artificial token

import { OpaqueToken } from '@angular/core';

let numbers = [ 1, 2, 3, 4 ];
let config = '{ "some": "json", "config": "data" }'

const NUMBERS = new OpaqueToken('app.numbers');
const CONFIG = new OpaqueToken('app.config');

Now we have tokens for the items we want to inject. When we configure the providers, we use those tokens, and when we inject, we @Inject(TOKEN)

providers: [
  { provide: NUMBERS, useValue: numbers },
  { provide: CONFIG, useValue: config }
]

constructor(@Inject(NUMBERS) numbers: number[], @Inject(CONFIG) config: string)

UPDATE

Now, with Angular 4, we should use InjectionToken rather than OpaqueToken