I'm not on Facebook (and can't really comment on their photo storage options but I think pictures are resized) but am quite an avid fan of Google. Picasa Web Albums was limited to 1GB of storage so it wasn't really an option for me either but I've since learned that Picasa now offers a form of unlimited storage for photo's (and more importantly, videos).
In summary, files under a certain size don't count towards your 1GB storage limit and videos up to 15 minutes won't either. If you reach your quota, all future uploads are resized to fit within the free resolution requirements.
From the Picasa FAQ, the 1GB free storage of photo's and videos isn't affected when uploads to Google products (including Picasa Web Albums, Blogger, and Google Maps) are within the threshold.
The threshold varies for Google+ subscribers and
If you've signed up for Google+
You can upload photo's up to 2048 x 2048 pixels and videos up to 15 minutes for free (i.e. no harm to your quota). All photos uploaded in Google+ will automatically be resized to 2048 pixels (on their longest edge) and won't count towards your free quota. All photo's uploaded to Picasa Web Albums over the free size limit will count towards your 1GB free storage and once you reach your limit, any new photo's uploaded to Picasa Web that are larger than the free size limit will be automatically resized to 2048 pixels (on their longest edge), keeping you able to upload your photo's.
If you're not signed up for Google+
You're limited to 800 x 800 pixels but the videos can still be up to 15 minutes. Once you've hit your 1GB quota all your photos uploaded will be resized to 800 pixels (on their longest edge).
Although this isn't yet the unlimited storage solution that other services offer (like Flickr), it is completely free so it's a good step in the right direction. Having all your videos up to 15 minutes stored online for free is great (and not limited to going through Youtube any more) and now you have - at the very least - a helpful backup facility to your primary storage service.
Hope this information helps ;)
Keep an eye out for a more comprehensive overview of the various photo storage services when I've managed to put them to 'paper' ...