The EOS M is a "mirrorless" camera -- not a DSLR.
In a DSLR, there's a 45º mirror in front of the sensor. That mirror bounces the image up into the "pentaprism" which flips the image right-side up and "normal" looking. This allows you to frame-up the shot, set the exposure, and focus. When you take the shot, the mirror swings up, the camera captures the shot on the image sensor, and the mirror swings back down again. DSLR stands for "Digital Single Lens Reflex". It's called a "single lens" because the camera only has one lens and both you and the imaging sensor look through the same lens. The mirror which swings up and down is called the "reflex" mirror. (see:
Single-lens reflex camera - Wikipedia, the free encyclopedia)
Point & shoots don't have a mirror. The mirror adds to the size of the camera body because it requires space in front of the sensor in order for the mirror to swing clear to take the shot. When the camera doesn't have a mirror the body can be much shallower (front to back). This is part of why point & shoot cameras are much smaller (the other reason they're much smaller is because they typically have rather tiny sensors.)
Another nuance of auto-focusing DSLRs is the focusing system. A point & shoot typically uses "contrast detection" focusing. "contrast" detection means the camera identifies how quickly contrast can change between adjacent pixels (typically across an "edge" in an image). The best example is to think of a barcode. If you take a photo of a barcode and that barcode is in focus, then the barcode is typically going to be solid black lines on a white background. That means every pixel in the image is either "black" or "white". There are no "gray" pixels. HOWEVER... if you deliberate de-focus the camera and look at the same barcode image, you'll see the black areas softly blur into the white... that means there are lots of shades of gray in the image. The goal of the focusing system is to try to find maximum contrast in the image -- which indicates that the image is focused. The analysis of the image is somewhat compute-intensive (more on why this is an important detail in a moment.)
In a DSLR, the camera uses "phase detection" focusing (although you can put the camera into "live view" mode which will make it switch to "contrast detection" focusing just like a point & shoot.) Phase detection focusing is MUCH faster. A partial prism splits parts of the image in a way which causes the image to appear fractured if the image is not focused. When the two parts of the split image align, the image is focused at that point. The computer can detect this VERY QUICKLY and it's not particularly compute-intensive.
This means that when you take a photo with a DSLR, the focus and shoot tends to be fast. There is very little delay. When you take a shot with a point & shoot, you may notice that the camera has a slightly delay (perhaps a 1/2 second) before the camera actually captures the shot (this delay drives action photographers and parents with small children crazy with frustration.) The delay is caused by the fact that the camera has to analyze the image to determine if it's focused and that takes a while because the analysis is computational intense. The manufacturer can make the camera do this faster -- it can be so fast that there's no perceptible difference. But speeding up a computer means you run it at a higher clock-speed. There is a direct relationship between clock speed and battery consumption. Also the near-constant use of the live-view on the back of a point & shoot tends to eat through battery power. A DSLR, on the other hand, can go quite a bit longer between charges.
Back to the EOS-M
The EOS-M is a called a "mirrorless interchangeable lens camera" (aka "MILC" which is pronounced "milk"). It has no mirror nor does it have phase-detect auto-focus (so it's similar to a point & shoot in that area). What it DOES have is the (a) the ability to allow you to change lenses for a more optimal lens and (b) it actually has an APS-C size image sensor. That's the SAME SIZE sensor that all Canon "Rebel" model DSLR bodies have as well as the 60D and 7D bodies (the VAST majority of DSLR cameras use APS-C size image sensors.) It also can use a lens adapter which allows it to use any lens designed to work with an EOS digital camera (and all functionality will work.) The EOS M does have its own lenses as well... but since it's a new model Canon only has a couple of lenses which are designed specifically for it.
The lens on a point & shoot cannot be removed and they also usually fold into the camera body when powered off. This makes the cameras fairly compact. The EOS M has a "body" which is roughly the size of a quality advanced point & shoot, except the lenses do not fold into the body. If you detach the lens and just put the body cap on, the camera is compact. But with lenses attached it's not particularly compact (not compact enough that you could just slip it into a large pocket.)
As the EOS-M takes DSLR lenses and it's the LENS which is mostly responsible for image quality, that means you can get the same quality images using an EOS M that you can get using a DLSR. (BTW, Canon wasn't the first to do this... the Sony NEX cameras are also "milc" cameras with APS-C size sensors. I believe Sony and Canon are, so far, the only two brands which offer an actual APS-C size sensor in their milc bodies. All other vendors use smaller (and sometimes significantly smaller) sensors. Physically larger sensors gather more light. Each individual photo-site on the surface of the sensor can have a larger physical size as measured in microns. Larger photo-sites means they are more efficient and collecting photons of light and it also means they'll naturally exhibit less digital "noise". So you would get great images from the camera. I've not used one so I don't know how responsive it is when shooting (e.g. is there much delay?)
For traveling across Europe, I agree that one "super-zoom" lens may be more ideal because it saves space and weight. Ultimately having "one lens" is usually not a good idea because the lens sacrifices image quality in order to provide a greater zoom range (lenses that zoom less -- or even lenses that do not zoom at all -- will typically have better image quality.) But this would mean you could get a convenient lens for travel and, if you prefer higher quality optics when you're not traveling you can always get other lenses later. You generally wont notice the image quality difference unless you're displaying your images in large sizes or making large prints. But if you really zoom in to inspect the detail, you'll notice there is a difference.
Whether you prefer a decent point & shoot (and there are some fairly advanced point & shoots) vs. a milc vs. a DSLR really will depend on how much of a premium you put on size & weight. The DSLR will, of course, offer the greatest level of adaptability, performance, and image quality, but it'll also take the greatest amount of space.