You can export from iPhone (and presumably from Aperture as well) to a folder. From there you can import to whatevergoogleisusingthisweek for photos. It was Picasa, then it was picasaweb. More recently I think it's google+. When I had a gingerbread Android phone, all my picasaweb albums simply showed up on my device. Once I moved to JellyBean and beyond, none of my photos show up there any more. It was kind of like Photostream backwards. I notice that when I take photos on my Android devices, I get emails telling me there are "new photos available to share" but I've never bothered doing anything about it.
Other alternatives are:
1 - Dropbox - costs money if you go over a few gig
2 - Smugmug - costs money
3 - Shutterfly - free
4 - Flickr - free
5 - Snapfish (not sure of cost)
Some of these have hooks in both iOS and Android photo management capabilities. Others have apps available.
Since you are a Mac owner, I struggle with how you would expect a S5 to be a better fit than your 5S. I find the way Photostream pushes photos to my Mac and caches them there until I "get around to" importing them in iPhoto to be effortless. I like the way quite a lot of my apps share data between my Mac, iPad and iPhone via either iCloud or dropbox.
As an iPhone 5 owner (iOS 7.1.1) and Moto Razr M owner (kitkat 4.4.2), I find I have a strong preference for iOS, despite the inability to read web pages in portrait mode. I will probably be near the front of the line when a higher horizontal resolution iPhone finally comes out though I've no interest whatsoever in a device physically as huge as a Note 3.