The Vita and console controls for Hotline work really well, but I balk at the notion that they're just as good as the keyboard and mouse, and especially wouldn't say that they work just the same way.
A mouse will always be far more accurate for aiming than a stick is, that fact has never been reasonably contested. The Vita has touch lock-on, which is a very innovative feature, but on PC I've never felt I've needed it. I've played the game 80 hours and I don't even know which button the lock-on is. The ability to look further using the shift button also helps to fundamentally differentiate the PC version. On Vita you accomplish looking around the map by dragging the screen. Again, very innovative, but you can't really do this while you're moving around, leading to a less active playstyle if looking around the map factors into how you play the game. On console you can look further while moving, but because the aiming is relegated to a stick instead of a mouse, the reticle always snaps back to your character when it returns to its neutral position. You can use the far-aiming in a more active way than in the Vita version, but it ultimately pales in comparison to the ability to drag the reticle without having it snap back every few seconds.
The vast majority of Hotline speedruns are done on PC, because they couldn't be done the same elsewhere. Everyone has their preferences, but if you're talking about accuracy and efficiency in regards to aiming, sticks can never stand up to a mouse.