Definitely allow sign up from both; being forced to use a web browser to sign up is an extra (particularly burdensome) step exactly when you don't want to annoy your user; before they're committed to using your app.
A great example of what not to do is the Live Tweet app on the Playstation Vita. To sign in and actually use the app, you have to go to the Twitter web site and log in through that, then write down a PIN to enter into the application.
Multitasking on Mobile is relatively painful, and often using a web browser is too, since Apps don't depend as much on the network. To this date I still haven't set up my PSA Vita to use Live Tweet because it's a massive pain in the butt.
The reason this is a problem is I just downloaded this app. I'm not "sold" on it, if you make it hard to use from the start it's extremely easy for me to just leave. I need to be able to sign up as easily as possible from wherever I start. That means any way I can first find your app; be it on the Web or in the App store, I need to have a painless first time experience.