Having used a variety of systems for quite a number of years, I gotta say I use the Lansky most often, but as it has been said above, it isn't my first choice for big knives. I consider a knife with a blade over 6" as a big knife. Anything under that and a Lansky works great. I have not used an Apex system, but I'd sure like to give it a whirl.
Josey has it right for sharpening small knives. I'll add this (and somewhere there's another thread with this same info) -- if you use a marker to blacken the edge of the blade and then very lightly run it across the hone, you can get a good indication of whether or not the angle is correct. How? Well, if the angle isn't right, you will either take the ink off just the very tip of the edge (and then the angle is too steep) or off the back of the edge (and then the angle is too shallow). If the ink is removed from the entire edge of the blade, ya got it right, Bucko!
The most important thing about sharpening a knife is to keep the angle consistant throughout sharpening. That is the number one reason why most people cannot get a sharp edge. Lansky, Apex, Catco, and other systems do that for you, and that's why they are so successful. Now, sharpening developes a very fine edge that is usually very brittle. Taken to an extreme, this edge can become a "wire edge," wire thin and extremely sharp, but curled over and fragile. It breaks off easily. Therefore, if you find that you are sharpening often but your knives go dull rapidly, this is probably what's going on. The good news is that it is easy to detect and easy to get rid of.
After you've put an edge on a knife, very (very!) carefully and very lightly run your thumbnail down the width of the blade (from spine to edge). If you feel the edge catch your thumbnail as it crosses the edge, you have a wire edge, since the edge has curled over. Think about it -- your nail can only catch if the edge has wired out since a proper edge should let your nail slide right off. Get rid of the wire edge by increasing the angle and very lightly run the knife over the hone. That should remove the portion of the edge that has curled over.
Now, how sharp do you want your knife? How fine should your hones be? Should you use a strop? All that depends on what you are going to cut. Cutting rope and cardboard a lot? Maybe you don't want to go for a super fine hone and stroping. Scary sharp edges are only good for fine slicing or shaving. A "working edge" that isn't so extremely sharp will last longer for heavy cutting. Working knives usually do not have thin edges and very shallow angles. If you are slicing tomatoes or cutting out newspaper articles or the like, maybe it's time to go for the finer hones and stroping.
How do you test an edge to see if it's sharp? A lot of folks shave the hair off their arm, but this is dangerous and more of a macho thing. Plus, it is a real good way to draw some blood. Don't ask how I know. Another method is to lightly run the edge over your thumbnail -- if it catches with no pressure, it is sharp! This is also not a very safe method. Again, don't ask how I know it's not safe. Safest method is to take a piece of paper about 6" long and hold it in one hand while lightly trying to cut it while it hangs free. If you can cut a free hanging piece of paper, you have a sharp edge.
Final thought -- sharpening knives and testing the edges can be a dangerous thing to do. Pay attention and don't try to show off. One little goof can mess up your whole day.