It's an excellent camera - the sensor is much better than that on P&S cameras, and keeps up with DSLR sensors in good light - obviously not quite as good in low light (though still better than P&S)...the lens is absolutely gorgeous - F2.8 constant, very very sharp even wide open, and about as good as one can hope to get - many interchangeable-lens Sony shooters who have tried the RX10 wish that exact lens was available for purchase for their cameras.
The obvious limitation though is the 200mm maximum reach. That's not much for birding - your typical superzoom cameras with 25x, 35x, 50x, and so on have wide-angle equivalents of 24mm to 28mm, and that '35x' means that the maximum focal equivalent is the wide angle multiplied by the zoom factor. Your SX40 is 24mm on the wide end, so 24mm x 35x equals 840mm. More than 4 times the maximum focal reach equivalent of the RX10.
That said, it's not ALL about focal length equivalence. Consider that your camera has 12 megapixels on a tiny sensor, and the RX10 has 20 megapixels on a much larger sensor - that gives the RX10 much more room to cleanly crop into the photo and still get good detail and reasonable file size for prints...You could essentially crop about 50%, which would give you closer to a 400mm equivalent result, at 10MP - and the shot may have more fine detail and less artifacts because of the better lens and sensor. If the light gets lower, the F2.8 lens of the RX10 and the better high ISO ability of the larger sensor will give it an advantage over the SX40 too.
It all comes down to when you will be shooting and how far away. If you typically photograph birds using full 35x zoom on your current camera, and still need to crop a little...and you shoot almost exclusively in sunny daylight, then you'll still be better off overall with the extra reach of your current camera. If you don't always need full zoom, shoot in lower light or overcast days, or live someplace where the birds allow you to get a little closer, the RX10 can be quite good.
Then again, another camera that might be worth a look in your case would be the brand-new Panasonic FZ1000. It shares the same 20MP 1" sensor size that the RX10 uses, which should enable it to be as good with high-ISO shooting...but it also uses a much longer-reach lens - 25-400mm, with a variable aperture of F2.8 at the wide end and F4 at the long end. This will give you double the reach of the RX10, but still half of your SX40 - but the extra cropping room and better performance of the bigger sensor may make up a good bit of that difference. It's priced lower than the RX10 as well. One advantage the RX10 still holds is that it is a weather-sealed body, which the FZ1000 is not - depends on whether or not that matters to your shooting environment.
I shoot with a DSLR and a mirrorless body for birding, and also have the RX10. I picked up the RX10 because the local store was closing and blew it out for 1/2 price - couldn't pass it up. It's a gorgeous travel camera and built like a rock. It's not something I would consider a 'birding' camera per se, but I have used it for some birding just to try it out and see how it did. Here's a gallery of bird shots I took with it, just for reference:
http://www.pbase.com/zackiedawg/sony_rx10
Remember too that I'm lucky enough to live in a place where I can get pretty close to the birds, so the 200mm lens limitation wasn't as impactful for me - I can often get within 10 feet of many birds. But I also discovered that the camera really does allow for a lot of cropping - and still retains excellent detail...so I would consider it reasonable at cropping up to 50%, or 10MP, and still getting very nice prints.
Hope all of that helps!