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My iPhone is set to upload all pics to Photostream, Aperture (in my case, iPhoto in yours), then automatically adds them to the iPhoto library when Aperture (or iPhoto), is open. No Dropbox required.

Dropbox is useful in this way if you want the same library content available to 2 or more Macs but bear in mind the comments regarding how long it can take to sync.

Also bear in mind using Dropbox as a backup has pro's and cons:

Biggest Pros are that the copy is offsite and automatic.
Biggest Con is that if you accidentally delete images, Dropbox will happily remove them from your backup too - not ideal (although DB has a restore deleted files capability, GD doesn't as far as I am aware)
 
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