Steadiness will depend on usage, what monopod you have, and where you are. They are a handy tool, but not really a full replacement to a tripod. Depending on the design of the monopod and the tripod you're comparing, there are some things that you can pull off with a monopod that won't work well with many styles of tripods.
I find my largest use of a monopod is simply to carry the weight of a heavy but otherwise handheld setup more so than directly adding stability. If I'm out birding with a 500mm lens, then I would often use the monopod to hold the camera up 'at the ready' so that my neck/shoulders/arms aren't getting tired from holding the weight while waiting for a subject to head where I want them, but then I would lift the whole thing off the ground when taking the actual shots. (The monopod then acts as a dampening mass hanging down from the camera while doing panning shots rather than trying to pivot myself around it - It just felt like I got smoother pans out of it.)
You can get very good stability from a monopod by using it as a pole that you wedge or pin down somewhere. I've used a monopod to hold a 4x5 for shots by doing things like pressing it up against a fence with my knee, wedging it in place and hooking my leg around it while sitting on a bench, lying down with the monopod pinned under me at the top of a knoll or on a large rock, or even sticking it in a tree and hanging my gear bag from it. I've resorted to such things in part because my carbon fibre monopod is smaller and easier to pack than a tripod, and doubles as a light walking stick far better than a tripod, but also mostly because the only tripod I own is in storage on the far side of the country and I haven't gotten around to getting one out here on the west coast yet.
A tripod and a monopod will always be limited in stability based on their construction and where you place them.
-The beefiest and most stable of tripods won't give you great multi-minute exposures if you plant it down on a bridge deck next to a running pile driver, and a monopod propped against a fence isn't going to give great stable results if there are a dozen kids using the rest of the fence as a set of monkey bars.