I work (as an architectural designer) for a construction company that is known for decorative concrete. We don't normally do residential projects, but we do "estates" (read: upwards of $1 mil on hardscape and landscape).
So, I will break it down for you. Cost, design/type (sealer, color, saw cuts/joints, maintenance).
Cost - In our area (the midwest), decorative concrete would cost $10-12/square foot, installed by union contractors. You can almost always find one of those same guys who will do it on the side for a bit of savings, but you won't have the reputation of the company (or insurance) standing behind their work.
design/type - there are different types of decorative concrete. the one you mentioned was stamped concrete, which yes, can be slippery. The main thing that makes it so slick is the sealer you use.
Sealer is put on to initially help in curing and to help "protect" your concrete, increasing longevity by protecting from the elements, such as salt, freeze/thaw, and UV (which can deteriorate not the concrete, but the color). There are 2 types of sealer (well, a TON more, but I'm explaining basics here): penetrating and film-forming. A penetrating sealer will "soak in" and give a matte finish. After it's dry, it many times, doesn't look like it's been sealed. The other kind is a film forming (also known as high solids) type. This kind sits on top and protects everything underneath is, much as a nail polish's top-coat. When dry, it will give glossy-ish finish (varying degrees depending on brand and formula)and enhance color, making more vibrant and giving it a wet-look. You can make it less slippery by adding a texturizer, such as "Shark-Grip".
Color: there are two main ways to color your concrete - stain and integral color. Most people use stains and then seal them in. This is the most economical. But as the top surface is worn, color wears off with it, exposing the regular "gray" concrete underneath. In unfortunate circumstances, if the sealer is incorrectly applied, the stain might flake off. If the concrete itself is "bad" (wrong mix, etc) and has pop-outs (where stones pop off the top, leaving pock marks), the grey concrete will be exposed, as the pop-out will have taken the surface-applied stain with it. If your concrete was properly installed, and maintenance is kept up, then this should keep the same look for years and years. One last thing about stains - the type they use and the surrounding area should be taken into consideration. We've seen where (other) installers used acid stains, and then used the chemicals needed to stop the reaction (we use plain old baking soda). Problem was when they rinsed them off, the chemicals ran off the edges of the driveways, into the grass. Homeowners could not get grass or any plants to grow there for years, and just figured it was "bad soil" or something. No, it was contaminated soil. We took that out and replaced it with fresh topsoil and it was good as new. The other type is Integral color, which can add as much as $100/cubic yard. in this method, color is mixed throughout the concrete, so if it wears, cracks, or pops out, color is consistent, not drawing the eye to the imperfection. If maintenance might be spotty, I would recommend this route, as it'll keep it's look for far longer with less work. There are ways to get around the cost difference (use the colored concrete for the top few inches instead of all the way through, and you save the $ for the color on the base inches), but all of those should be discussed with your installer. If they are not familiar with those methods, they can lead to disastrous results. Both the types of color can be enhanced with shake on colors (sometimes containing hardeners) to create a more dimensional look.
Saw-cuts/joints - joints are placed in concrete to give the concrete a suggested place to crack. Because it will, no matter what you do, crack. Joints are placed every 6-12 feet, depending on lots of design factors. The installers will either make indentions while the concrete is wet (joints), use them as pouring start/stop points in their forms (also a joint, but a cold joint) and will put expanding foam in between, or may cut them after the concrete has cured (cuts, or saw cuts). Many designers can use the joints in a pattern (like a sidewalk "square"). We have used them as curves and lines to make pictures - we did a job at a high school and made their mascot, a wildcat - it looked awesome! , create designs, delineate different types of textures, stamps, etc. Imagine joints or saw cuts as your black marker when a cartoon is drawn. Then concrete acts as the markers to color in between the lines.
Maintenance - concrete is as close to maintenance free as you're going to get for a hardscape. You may need to powerwash and seal it every few years to preserve the look of a stain, or even restain and reseal. It depends on your design and installation. Installed properly, it will never need the type of attention that say a wood deck or paver patio (having to sweep in new sand in the joints) or an asphalt drive would have.
Obviously, I work with this stuff day in and day out, and if you can't tell from my examples, we are called in often to "fix" a problem installation from someone else's screw up. Done right, concrete can last upwards of 25 years.
last piece of advice: if going with concrete, decorative or otherwise, please, please PLEASE hire someone that has experience! There are so many people that have a pickup truck and will rent the stamps and buy the concrete. Yeah, they CAN do it, but it doesn't mean they should. Ask for references, and ask to GO see places they've installed. Look for pop-outs, cracks, sloping. Look for consistency in the stamp pattern (depth, not blurry), and also variation in direction (so it's not the same thing over and over and over in the exact same repeating pattern... most stamps are made to fit in more than one way so the patio can look varied, not cookie cutter.). Ask previous clients if they were happy with the work, how clean they left the jobsite, how the follow-up and maintenance has been. in short, if they've never done it before, DO NOT be their guinnea pig - it's too $$$ of an investment for something that "might" turn out ok.
Any questions - feel free to ask!
Sorry so long, but I was trying to arm you with proper info.