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Java is a safer bet than Silverlight overall though, at least(especially for non-Windows users), but it's less likely to be readily installed when the user visits your web-app. it would require users to not only visit your site, but to also install a browser extension with extended permissions to access native APIs.
So they not only need to install something, it needs to be tailored for the right browser. I'm not saying these are great options, I'm just saying it can definitely be done.
Thus, Flash (and Shockwave) were more or less the no-brainer approach to doing this.
If you want to use either of the first 2 alternatives given above, the problem you'll hit is that it's less likely that users will have already installed the plugin.