I wouldn't say they are very similar, no. I suppose they are mechanically similar on the surface, in that you hit level cap, run dungeons (strikes) to gear up, and then run raids, but with loot games, it's all about how the fine details play with player psychology, and I think that's where Destiny falls flat on its face.
Gearing in Destiny is fun from 1-20, but at level cap, it's almost entirely frustrating. You are basically doing random things for a chance at random gear.
In WoW, you had loot tables for each boss, so while you still might end up getting zippo from the raid this week, you have a sense of build-up and excitement when you get to the boss who has that one sweet helmet upgrade you've been waiting on. Same thing for dungeons: yes, you might not get that sword from Rend Blackhand this time, but you have the excitement of "I hope he drops it this time!" and you have that sense of focus, the "okay, I'm going to place X to hopefully get armorpiece Y".
Destiny has none of this, and what's worse is that the random item you might get is often not useful for you at all. You're running a random strike, to maybe get something you don't even want or need.