While both Skype and Gmail store your messages (if you Skype across multiple devices, you'll see logs of conversations that happened on different devices), I don't think Gmail probes every URL you send in your messages. Also, SMTP is not always done under SSL, so, privacy cannot be assured.
But that's easily testable. I'll get back to you in a couple hours.
One automatically scans your email to show related ads, another does a HTTP HEAD request to URLs for only the server headers, which they say is for malware scanning purposes. Both are automated jobs.
See my other post to see how Google employees have access to all your email, documents, chat transcripts, Google Voice calls, Youtube videos etc. and how a few abused it to stalk teens.
https://news.ycombinator.com/item?id=5728707
As usual, Google gets a free pass and Microsoft gets demonized(they should stop claiming it's end to end encrypted, though). Looking at your HN profile, it's not hard to understand why. Thanks for being honest about disliking Microsoft but please try not to let that color your objective opinions and playing favorites regardless of facts.