Like you, I am an Apple user, having an iPad and an iPhone 5 as well as two Android phones, an HTC One and a Samsung Galaxy S2.
I had an S3 for a while but got rid of it as it was just awful. Shocking battery life, force closing apps and so on. I won't go into details. My S2 however hasn't missed a beat even if it is old and battered and due for retirement shortly. My HTC is amazing. Simply the best phone I have ever had the privilege of owning. Better than my iPhone 5 by a country mile. Don't get me wrong, I love my iPhone but the HTC One is better for all the things I want to do, on a screen that puts the iPhone to shame.
So, basically i've had a mixed relationship with the Galaxy range over the years and so I am coming to the Note 3 with similar misgivings as your good self.
However, what I usually do is research a subject exhaustively before I go ahead and part with my hard earned, much like you are doing.
With regards to battery life. On my HTC I have everything turned on, GPS, location services, push mails and the like. My battery is incredible. So far it is coming up to the end of the second day of life still with 58% left. My iPhone just cannot keep up with that and neither can my SGS2.
I don't use any task killers at all. I did on my SGS2 and found that they didn't help the battery life at all. in fact they did the opposite. Maybe once upon a time you did need to use them but with the advances in battery tech over the last year, I really don't think you do anymore.
My advice to you is this: Don't buy a Note 3 on day one. Wait and see what people say about it first. However, please bear in mind that more often than not people only seek out a web forum to post up if they are having issues with their device, not when everything is going swimmingly, so take a lot of those posts with a small amount of salt. The best thing you can do is to see if there are any trends, read the professional reviews and comparisons and just ease into it gently.
My SGS3 was a 'day one' lemon of a phone and I couldn't get shot if it quick enough. My HTC was a day one phone too and it's not dropped a single beat in the months since i've had it.
I've been umming and aahing over the Note 3 but i've just had a windfall of £400 so i';ve decided to retire the SGS2 and replace it with the Note. I'm going to hold off on the Galaxy Gear until they improve the looks and battery life though.
I hope this helps.