So, I'm currently leaning no on getting Destiny, especially at launch. But I've been hearing about the deal where if you buy the last gen version, youl'll get the next gen version free. Does this mean that I technically own it on both current and last gen? Or does it mean that I can upgrade it to the next gen version? 

You have both versions as long as you purchase the PS3 version, then purchase the PS4 version free by January 15, 2014.  Same for 360/One.

"When you buy/redeem the Destiny Digital Base Game, Digital Guardian Edition, or Expansion Pass on or before January 15th, 2015, you can download the Playstation®4 version from the PlayStation®Store for free by doing the following:

- Log into your PlayStation®4 using the same Sony Entertainment Network Account (PSN ID) used to buy/redeem the Destiny digital content on PlayStation®3.
- Navigate to the Destiny content page or search for the corresponding item you purchased previously on PlayStation®3.
- Add the item to your cart and complete the transaction.
- Wait for the download to complete.

Expansion Pass content (which includes Expansions I and II) will only be available for full download once released. "