from a high.level point of view: web software development needs more focus on non-functional qualities, like stability, responde-time, performance and so on. Reason: Users of expensive rich-client software are somewhat bound to that software because of their efforts when acquiring and installing their software. Users of web software are less tied to a sepcific web solution and quickly become annoyed when the web software responds slowly or strangely or not at all. Read Prof. Jeff Offutt's papers from George-Mason-University - I one met him and his work is impressive !
To add what Georg Heidenreich wrote, the web software has early release cycles. Also the interface needs to be updated frequently since user needs rich interface that responds quickly.
To add to both Sanjeev and Georg's remarks, web-based software development is often much cheaper (often free) than its counterpart. I suppose the infrastructure encourages the creation of the sort of excellent open-source platforms that professionals now regularly use to initiate, produce, and ultimately deploy their products.
On the other hand, the fact that there's still a big market for "conventional" software dev platforms suggests that open-source web-based dev has some catching up to do in terms of producing products of comparable robustness. (But I do wonder whether the line between "conventional" and web-based is even clear anymore). I can't think of any conventional platforms that haven't also fully embraced what the internet/web has to offer to leverage their products to an even greater extent (e.g., MS Visual Studio TFS). I'm a relative novice, but that's just my two cents.
When doing Web development, the "go live to customer/user" cycle is significantly compressed, and much more conducive to Agile development models - relative to an application that one installs on a server. The feedback from the user community is also almost instantaneous.
If the website is used by millions (I'm thinking facebook, ebay, etc), simple GUI changes will attract legions of users who like it and many who will request that you change it back.
There are a number differences mostly related to scale, performance, security, resilience, failover, uptime and so on. Systems developed for small numbers of users or install bases often do not need to meet those kinds of demands, whereas web systems must meet them all.
Furthermore, web apps need to meet usability constraints far in excess of most other kinds of apps: every kind of device, browser, platform, not to mention languages and input methods.
Web apps often need to cope with enormous variations in load too. For example, online betting systems often cope with spikes 2-3 orders of magnitude larger than their everyday normal use. Being able to spin up and down servers automatically on demand is a must.
Whilst some answers here correctly identity that the lead time from idea to delivery can be quite short on the web, other kinds of apps are adopting the same practices to allow them to be competitive and responsive as a business. For example, banking applications need to be robust and respond to rapid changes in business demand.