Yes, the iPad & iPhone apps could be more fully featured, and I hope things change on that front in the future. I still use them for reference or small stuff if I'm out and about.
However, if you want fully featured Asana on your mobile, you can choose "Request Desktop Site" in the browser. Here's how (with screenshots below):
Safari for iOS. Navigate to https://app.asana.com, then hold your finger on the refresh icon. Click "Request Desktop Site". Done.
Chrome for iOS. Navigate to https://app.asana.com, then tap the More icon at far right. Click "Request Desktop Site". Done.
Due to the nature of touch devices and the way interaction is done on websites, though, the web app is kinda frustrating to use for checking off tasks and such. Thankfully, I can spend most of my time on my laptop and in the iPhone app to get things done.