I've only been playing with dslrs for c 20 months, and with Canon's for only 4, so my comments may be worthless; but I was recently in a situation not entirely dissimilar to yours, so here goes. I started out with a Nikon D3100 and while it seemed like a good camera, I always got the impression that I could be getting better results (for reasons in addition to my inexperience) - plus, I wasn't entirely pleased when the autofocus mechanism in the camera died after four months (Nikon promptly fixed it, but still...). So I started reading more, looked at lots of comparison sites online, etc. and ended up with a Pentax K-5 which, at least in terms of sensor quality, is probably as good as crop-sensor dslrs get (it doesn't hurt IS is in the body either). I could see easily enough that FF cameras could give better results, but at the time I decided they were beyond what I wanted to spend, so I ruled them out. The K-5 proved to be a good buy, and obviously better than the D3100 in every way.
But of course I kept reading about the superiority of FF, along with arguments to the contrary, and decided I needed to find out for myself. The D800 and 5DIII had just been announced but wouldn't be available for a while, and being impatient I decided to rent a 5DII, telling myself that if I couldn't produce better results with a 5DII than I could with the K-5 I would stick with the K-5 and forget about FF altogether; how much better would the D800 or 5DIII be?
A few days later a 5DII plus 24-105L showed up and after an afternoon spent comparing the 5DII and the K-5 it seemed pretty clear to me that I "needed" FF. It became even more obvious when I took photos indoors outside that night (I like low-light photography). Shortly thereafter I bought that 5DII/24-105 combination, followed by a few primes, a 17-40L and 70-200 f/4 L IS, and a flash, along with a Rebel as back-up, have almost finished selling off my Pentax gear to help pay for it all, and haven't looked back.
(By the way, those who complain that switching brands is expensive overstate the problem, I think - where I had bought Pentax equipment new, I didn't lose much, and where I had bought it used I *gained* overall, so I ended up having paid very little for a year's use of an extremely good camera.)
Of course, comparing a K-5 to a 5DII wasn't quite the same as comparing a crop-sensor Canon to a 5DII since I didn't have the same lens on each camera, but now that I own a 5DII and Rebel T3i I'm pretty sure the differences are similar (I also suspect that the Canon lenses I've ended up with are better than the lenses I was using on the Pentax, but that's another matter), and all in favor of the 5DII except size/weight.
As for Daniemare's questions, they're hard to answer because it's all rather subjective. Yes, this stuff's all heavier than most of what I used to carry around. I took most of my Canon items to Paris with me in May and often carried around a bag containing the 5DII plus 17-40 + 70-200 or just the 24-105 and must confess that by the end of the day I sometimes felt like tossing the whole lot into the Seine. But (1) I have a back which tends to tire easily and I used to sometimes feel like that carrying around the lighter Nikon and Pentax gear; and (2) when I got back to the hotel and looked at the photos I decided they made it worth the effort. When I'm not in tourist mode, carrying equipment around all day isn't an issue and I've discovered that by far the easiest way to carry the 5DII is to hold it by the grip without a strap attached; no matter what lens is attached, the balance is excellent and it doesn't seem heavy at all, even when carrying it for hours (I've long since gotten over the fear of dropping it). Your experience, of course, may be quite different - for all I know, your back is much better than mine, for one thing.
The flash issue is subjective too. I much prefer natural light to flash and on the rare occasions when I do need to use flash I'll use an external flash; I don't like using built-in flashes - sure they're convenient, but to these eyes nothing looks good hit with the light they provide. So no, I don't miss it at all on the 5DII! You might, though.
Most important for me is whether I can notice a significant (to me, obviously) improvement in the photos I want to take in the manner I want to take them (e.g., I never do video, use center-point focus only, and don't care how many shots per second a camera can take, so all sorts of features that plainly matter a lot to other people don't matter to me at all). I was able to answer that question pretty quickly when I rented a 5DII. If, like my father, you aren't at all interested in low-light photography and dislike shallow depth of focus, your answer might well be the opposite of mine.
So I can only echo Marshall's advice: if you don't know anyone who owns a 5DII and is willing to lend it to you for a few days, and if it's an option (it's easy to do online in the USA), rent one - it's the only way you can really discover whether it will do a better job of what you want a camera to do, whether it's inconvenient to carry around, and whether any improvements you notice make that inconvenience worth while. No, it's not free, but who knows - you may end up saving a lot of money!