I've tried both and been successful with both (probably most successful with calorie counting).
For me intuitive eating is probably the riskier strategy (because my intuitive eating got me upwards of 220lbs and I'm under 5'1"), but on the other hand, when I calorie count I have a tendency to get uber-obsessed, and I don't think that's especially healthy either.
My philosophy has changed beyond all recognition from how it was back in the days when I'd weigh and measure every food item and ingredient (even a spoonful of Splenda) and scrutinise food labels for information on fat and calorie content.
For the past 5 years I've been gradually and progressively cutting more and more of the crap out of my diet (whether I'm actively 'dieting' or not). By crap I also include stuff that was on even my strictest calorie control lists only 5 years ago (stuff like diet Coke, or low fat yoghurts flavoured with aspartame). It's been a very gradual process - so much so that I've hardly been aware of it - and it's brought me to a place that's almost unrecognisable from my point of embarkation.
My food rules are very strict, and have their foundation in a lifestyle ideology, rather than a weight-loss ideology. Of course weight loss is important (for health reasons, if for nothing else), but nowadays it plays second fiddle to my primary goal of eating in a natural, healthy, ethical and environmentally responsible way.
Nowadays I only eat food that is organically and ethically raised, not genetically modified in any way, produced within 50 miles of my home, as unprocessed as possible, and not packaged in plastic.
This choice of eating is expensive, so it's forced me to waste far less food than I ever have before. I used to waste a TON of food...mainly stuff like fruit and veggies, that went bad whilst I ate chocolate and fast food instead. Shame on me!
So now I buy less food, waste less food, and eat food that's of much better quality than I used to previously. And my food choices are hugely restricted - which could be seen as a bad thing, but I've chosen to see as a positive change, because it's led me to better eating by default, since most chocolate, confectionary, processed food, fast food etc. isn't available in an organic variety or produced within 50 miles of my home. And even when it is, it's almost impossible to find it packaged in anything other than a plastic derivative. So, I have a very narrow selection of foodstuffs to choose from, and this practically guarantees that my diet is centred on whole grains, veggies, pulses, fruits, nuts etc. I think of these as superfoods, because they're nutritionally dense, natural, beneficial to the body, and none damaging to the environment.
Since I've adopted this way of eating I've stopped counting calories, and I rely on intuitive eating to ensure that I get the right balance of nutrients whilst keeping my weight in check (and hopefully heading in a downward direction).
Of course even eating these superfoods could cause me to gain rate at an alarming pace if I were to eat them without any form of restraint...so though I don't count calories and usually don't weigh food either, I pay very close attention to my portion sizes, and I NEVER EVER eat to the point of feeling full. This was a hard thing for me to learn, because like mkendrick I too used to think that my 'full' button was broken...and I had to re-learn the signs and signals of satiety...and I can attest to the fact that satiety is something that can be re-learned (or learned for what appeared to be the first time, in my case!

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Ultimately, it'll take a while for me to assess whether or not this is working from a weight loss viewpoint, and if it isn't and I find I'm either gaining weight or maintaining this unpalatably high weight I'll maybe have to make a few adjustments. Ultimately, though, they can only be minor because this is (for ethical and ideological reasons, NOT weight loss reasons) the way I want to eat for the rest of my life.
So the eating habits are none negotiable and not majorly tweakable...so if I seem to be heading in a direction I don't like I'll just have to spend more of my free time exercising to pick up the slack!