It does a ton of things, but in this specific case you can easily send links to yourself with one click and then instantly access them on the other device.
Do this:
1.) Create a Linkdrop account
2.) Click the cog/settings icon next to "My Bookmarks" once you are logged in
3.) Drag the green "My Bookmarks" button/link to your bookmarks toolbar
That's pretty much all you need to do. It will add a "My Bookmarks" shortcut on your bookmarks bar in your browser. There's nothing to install.
Then whenever you are on a website that you want to look at on your other device just click that "My Bookmarks" button on your bookmarks bar and it will save the link automatically to your Linkdrop account with one click. You don't need to do anything else.
Then just open Linkdrop on your device (I have it as a shortcut on my phone) and click the link. It will be at the top of your collection.
Make it pretty simple. Visit website on computer... click "My Bookmarks"... open Linkdrop on device... click the link. Done. With just one click on the computer and one tap on the device.
You can also drag the "Drop" bookmarklet from Linkdrop to your bookmarks bar which will put a "Drop" button on your browser bookmark bar. Clicking this button when on a website will open a window allowing you to choose which folders to save the link to. This way you can choose "My Bookmarks" from the list and also any other folders, such as those shared with other people you've added. If you don't choose any from the list it will automatically save to "My Bookmarks". This way you can use the "Drop" button when you need to send to multiple people, but can still quickly send to "My Bookmarks" by just not selecting any folders. I have both the "Drop" button and a "My Bookmarks" button in my bookmarks bar. The "Drop" button can be found on the "help" page link or by choosing "Browser button" from the settings menu in the upper right of your account.
(NOTE: SSL protected pages won't allow the "My Bookmarks" bookmarklet to save the link since it is a third-party script from another site, so you need to use the standard "Drop" bookmarklet for SSL pages and choose "My Bookmarks" from the list. Two clicks instead of one, not a big deal, but this is because web browsers won't execute a script from linkdrop.com on another website when the other website is secured by https/SSL.)
So, you can create a custom bookmarklet for any folder you have to add links to it with one click and/or use the regular "Drop" button to open a list of folders to choose from.
You can also email links to your library by setting a username in Linkdrop and then emailing links to your username @linkdrop.com
This is great if you're on a mobile device and want to save a link or send it to your computer. Just click share on your mobile device, choose email, send to your username @linkdrop.com and the link shows up in your library in a few seconds.
Anyway, click "Show features and more information" on http://www.linkdrop.com/ to see everything it does.
It creates a backup screenshot of every link, indexes the text so you can search the full body of your bookmarks instead of just titles, lets you backup YouTube and other videos to your account, connects with Dropbox and backs up your library, screenshots, videos, etc to your Dropbox account, allows you to share with others, lets you send links to Facebook and Twitter, and lots of other stuff.
Alternative -- write a daemon on each end of the circuit that updates a cloud database containing shared links. Then read the cloud shared-link database on each end. Such a scheme will work, but you have to write it yourself.