Both is important. But generally if you could only spend on lens or body and could only pick one, I'd pick lens. But that also depends on what you use it for. If you're shooting under bright light and still subjects, invest more in lenses instead. (Since you won't really utilise more expensive bodies) If you're shooting fast paced events with subjects that move a lot under really bad/low lighting conditions get a good body. (Because you'll utilise the higher fps, better noise control at higher ISO etc) The lens or body doesn't really control the photograph, it's the photographer. (Quite cliche to say it now, but it's damn true)
This to me harks back to the age old obsession with camera kit rather over technique.
Both the body and the lens play an equal part in ensuring the correct image quality when the appropriate combination is selected for the subject at hand. Even if you bought the most expensive body and lenses available then simply expected them to work for any subject you'd still end up with poor shots if you don't understand how to apply them.
The real skill in producing good images comes from the understanding of the correct application of the kit to achieve a particular type of shot. Plenty of top notch photographers out there could probably use a $50 film camera to whip the arse of someone with $10k bag of the latest digital kit because they know exactly what's needed to attain result they seek. That's not to say that buying a really good bag of kit is pointless, just to say there comes a point where it starts to make less difference how good the kit is and starts becoming an issue about how good the photographer's skill is at working with the kit.
Full Frame cameras are best in low light situations, or situations where you need the widest angle of view that you can get. Crop sensors perform well in portrait situations or macro work. As has already been stated by a few here already, the lens will affect the clarity and overall quality of the image more than the camera itself. Some cameras will allow you to get the exposure properly more easily, but for the most part clarity is determined by the glass.
got it right. If you want the best possible combination for each photographic situation, you'd need several bodies tailored at different tasks, while also having many different lenses, each made specifically for that situation. So yeah, for wanting the best of everything, and you shoot everything, 15 isn't far fetched, in fact, you might find yourself with over 20 lenses. As for bodies, well, a body tailored towards a sport shooter is gonna excel in sport shooting, but it can't beat a body tailored at studio shooting, and vice versa....of course, that's not to forget other equipment you might need...even a good strap is essential if you plan on carrying the camera with you all day long.
That said, unless you're a pixel peeper, have lots of money, or are doing certain type of photography for paid jobs, you can get by with one camera and 2-3 lenses.
I'd say the lens. You manipulate your cameras settings to get a proper exposure, but the lens is what determines what you see, be it close or far, with shallow or deep depth of field, etc. lenses all the way!