close-up wildlife

I have played with both cameras, and I would have to say the Fuji X10 has very high resolution macro shots that are very close up (1 cm and sometimes closer in bright light!). The colors on the X10 are also much more vibrant. I would definitely recommend it to someone who loves close-up wildlife photography.

For macro, the X10 is hard to beat. Fuji has just announced the X20 which shares the same optics, but a different sensor type, you might keep an eye on that.

However, owning a X10 myself, if you can obtain an X10, you won't be disappointed 

I've not used the G12 but what I can say about the X10, while I love mine to bits;

...most things except macro photography!

We want be shooting at the longer end of the the lens, 60mm-112mm but the X10 just won't do that.

I can offer some insight about the Sony RX100 and MFT.  The lens on the Sony is good for close-up work, but the built-in lens and flash combo don't always work well together.  The flash power can be easily reduced, but when the lens extends, it blocks some of the flash.

If you have your own light, or are using sunlight, the Sony RX100 can be a very lightweight option.  If you are going to get a sophisticated flash, then go ahead and get a micro-four-thirds camera.  The Panasonic G5 is excellent, and the Olympus OMD-D may be even better.

The key here is the lens.  Panasonic makes a 45mm F2.8 image-stabilized lens that is nothing short of awesome.  It will run you into about $800, but it does amazing macro work, and amazing landscape work as well.  I am not an expert, so you may want to read up on the reviews, but the pictures I have seen are uniformly excellent.

The downside is that you would be investing more in the lens than the camera.  If you look closely at the life-span of cameras compared to lenses, though, this is a completely rational idea.  A really good camera will be out of date in a year, and ancient in five years.  A really good lens will hold its value much longer than any camera.