The downside of the Web approach for mobile Building smartphone apps with HTML is a fairly painless way to create cross-platform applications that can tap into the deeper parts of the native API. I've built several applications this way and found that they usually worked on both iPhones and Android smartphones with no changes.
Still many of the complaints of mobile developers who write in Objective-C or Java also revolve around juggling resources. The little handsets have so much less memory than desktops and it's always a challenge to deal with them, whether you're doing native or Web app development. Don't take the issues I raise as being reasons to try the Web app approach. After all, the several hours you might spend monkeying with CSS is nothing compared to the years that some people have devoted sweating with pointers and memory issues. For the hours of work they take, the HTML apps can be stunning successes.