I have said that Warframe is the better game all along. I’ve played about twice the time in Warframe, but did finish the campaign of Destiny. The big thing Destiny has over Warframe is gunfeel. They aren’t going to be able to compete with Bungie in that area. However, everything else they do is fantastic.
It is a free to play, though I haven’t encountered any areas that kept me from playing for free. There are timer delays when crafting, but there is no reason to use paid currency to speed that up. Also, you can get the paid currency by trading in game with players, often selling items you don’t need to fuel your purchase of cosmetics. While I have bought platinum, the paid currency, it was more out of thanks to Digital Extremes rather than a need to get it.
Also, everything looks freaking rad in Warframe, and I don’t feel that way about the look of Destiny. Try Warframe if you haven’t. You’ll need to use a wiki, but it is well worth it if you like third person action.
Edit: I just noticed you said you haven’t tried it. Give it a go! It is free on PS4, PC and Xbone. I do suggest you use a guide from YouTube to help you figure out mods. iFlynn’s beginner guide helped me out a lot and tacticalPotatoe is another great resource.