I used to be in the camp that said that cartridge was 90 percent and TT only 10 percent.
A properly set-up LP12 (which I still think must be the most over-hyped item in all of audio, except Bose... but which is nevertheless a very nice TT) made me start to doubt that conclusion, and re-plinthed Lenco 75 and Garrard 301s (not mine!) made me fudge the percentages a bit more towards the TT.
The GT-2000 made me re-think the whole premise. I think Melofelo was right: what is required to make a TT that REALLY does what a TT should do is not simple nor easy nor cheap. When you get to the level of one that DOES do it all well, the impact is surprisingly big. Frankly, I'd rather hear an average cart on this TT than a superb cart on a mid-fi TT. But the number of TTs I've heard that I would say that about can probably be counted on your fingers, and living in Hong Kong I get to hear a lot of truly world-class TTs.
And incidentally, this qualifies for the OP's stipulations, as this TT comes with a tonearm, and it isn't designed to have interchangeable ones (although they did offer two alternative arms, and some people still manage to change arms on them, it takes some kludging).
Another digression: When speaking of "Ivor slugging around his first prototype to audio dealers in the UK to compare against the ubiquitous Jap DD tables, and proved that it sounded better," make sure you note the word "ubiquitous", in the context of the UK where he was. Back in Japan, they soon had DD TTs like this that send the LP12 figuratively into a fetal position in the corner of the room, whimpering, even by Ivor's own measures of PRAT, etc... NOT an easy feat, but the Japanese did accomplish it! Ivor didn't really "prove" anything, except perhaps what a clever marketer he was, and what the Japanese really thought of the British market.
Of course, the real answer to the OP's question is BOTH. If you have limited money to spend on the combination, I'd still recommend getting a better cartridge and tweaking a mid-fi TT. At the lower TT levels, the biggest gains come from upgrading the cart, not the TT, and good tweaking to get the most out of the TT will bring better bang-for-buck than simply buying a better TT.
But if your plan long-term is to go for truly high-end sound, then consider investing in a really good TT first, and then upgrading the cart, etc... I think Theophile discovered the wisdom of this approach when he was deliberating about whether to upgrade by getting a high-end cartridge for his PX-2 (already a pretty good TT) or by upgrading the TT to a GT-2000. He went for the TT first, and hasn't looked back. Go read his comments from when he first got it, if you want to read what someone else who has heard the difference a really good TT can make says.
As with the discussions of tubes vs. SS, source vs. speakers, or between driver types or speaker types, the answer isn't entirely black-and-white. At the level the OP is talking about, I'd still say cartridge outweighs turntable... but only because there are few affordable turntables that really perform well above average, and to get them, you'll still spend more than you'll spend on all but the REALLY high-end cartridges.
The proof? What is the most you can spend for a turntable? What do audiophiles pay for Continuum Caliburns, Rockport Sirius IIIs (if they can find one for sale) or Clearaudio Statements, etc...? And what is the world's most expensive cartridge? The prices at these levels are not just hype; it DOES cost a LOT more to make a TT good, than it does to make a cartridge good! If you limit the turntable choice up-front to mass-market models with built-in tonearms, then by definition you are limiting the quality of the turntable. At that level, you can certainly get more from moving to a better cartridge, than from a change of turntable.
