Firstly, I didn't realise it was a competition, and secondly I'd never boast of being eccentric - it's a trait generally seen as negative by most people, in my experience, and it's rarely meant as a compliment.
I agree with Econimica that Ni is 'wierder' than Ne, in that the INxJ's I've known - especially the F's - have often had me scowling and shaking my head with incomprehension at the way they seem to see the world, the crazy ways they make decisions and judgements and stuff, their odd little paranoias etc. I think that Ne tends to at least have itself grounded somewhere in the real world, though it's often nowhere obvious, whilst Ni can easily have a person spiralling down in their mind with all kinds of crap that has no basis in fact or experience or the world generally. So whilst I can usually find some way to get people to relate to my odd perceptions and behaviours, I find it very hard to sympathise with much of the way my INFJ friend sees things.
Though I'm sure it'll be taken the wrong way, I have to say that I think the differing styles of eccentricity between Ne and Ni are viewed as either positive or negative depending on who's looking at them. Someone to whom 'the establishment' is important and valued would probably find Ne style oddness more offensive, whilst someone to whom spontaneity, cheerfulness, trust and optimism were important would find Ni style oddness extremely irritating and hard to live with (as I do at times, so I've never lived with Ni-dominant types!).
The ISTJ I've talked about often on here is definitely very eccentric, and although I'm constantly called it by just about everyone, I do think there are differences in the 'tone' with which people say/mean it. It's like I said earlier, there's the misanthropic, anti-social kind of Silas Marner eccentrism to which Sensors seem to be more prone, and then there's the 'out there' and loopy kind like Q. And several shades in between.
How each person judges or reacts to these different kinds of oddness depends hugely on their own values and opinions.
And then of course, you have to draw a line between genuine eccentrism - natural and instinctive behaviour that comes from who you really are inside, though you might not realise how others see it, and you can't really do anything but that. Or the kind of false eccentrism which is put on to get attention or because someone wants to be seen as 'individual' or outrageous.
My experience is that those who wear their eccentricity on their sleeve tend to usually be the fakers. REAL eccentrics are the way they are through a lifetime of strange experiences and suchlike, and they've known since childhood the pain and other sides that come with the attention or whatever, of being known as 'odd' or 'different', and so have generally learned to cap it somewhat, and to appear normal-ish. And they don't say things like "I'm just mad, me!" etc., because deep down they do not believe themselves to be crazy or odd. They usually find it just as odd as others find them, that others find them odd!!!
EDIT - and people who say they're eccentric, but then also say things like "well what's normal anyway? is there any such thing as normal?" are 99% of the time not eccentric. Anyone who is, and has always been, knows that there is such a thing as normal, and that they're not it - normal is that elusive something that abnormal people usually spend the first part of their lives struggling to be without success, on account of which they've suffered and tried. Only people who are normal would claim that there's no such thing as normality.