Different sweeteners produce different results when used in baked goods and all sweeteners be can swapped for another in some capacity. This I know because I do it all the time, both to affect flavor and texture of food in various ways.
As for substituting sweeteners for health reasons, some may say that no sweetener is healthier than another (I'm not talking any zero calorie substitutes here). It's true that sweeteners all have about the same number of calories. It is a fact, however, that different sweeteners affect your blood sugar in different ways, therefore each has a much different glycemic index (a measurement of how quickly sugar from food is absorbed into your blood). I've done quite a bit of reading on this and find that the big picture put simply is fascinating!
Here's a quick synopsis of the real deal as I have come to understand it. A "Health Effects of Sugar for Dummies", if you will: Assume you're consuming sweets on an empty stomach when the sweetener is a large portion of the ingredients in your food. Table sugar will spike your blood sugar faster than pure maple syrup, which hits you a little faster than honey, which is faster than agave syrup, for example. Combining the sweetener with fiber, protein or whatnot will slow the absorption, as will whatever else is in your stomach. When your blood sugar levels skyrocket, such as drinking a big glass of juice or eating a heavily frosted cupcake, your pancreas releases a bunch of insulin to carry sugar from your blood and move it to your cells. When your cells feel overwhelmed (with a long term high sugar diet), they begin to resist insulin. This forces the sugar to hang out in the blood stream so your pancreas pumps out more insulin to clear it. When your body is constantly calling for insulin, eventually your pancreas may give up or slow down insulin production. Type 2 diabetes is caused by all of this, and on the bright side, a balanced diet and exercise (exercise encourages cells to absorb insulin) will help Type 2 diabetes from advancing. If your pancreas hasn't given up completely, medications can help with those who's cells are insulin resistant. In bad cases, insulin injections are required to manage Type 2 diabetes. While Type 2 diabetes comes from our food upsetting our cells, which upsets our pancreas, Type 1 diabetes is a failure of the pancreas to produce insulin (from genetics or a pancreas going out on you at some point in life).
It's also interesting to note that it is possible for fat cells to take up sugar and convert it into fat molecules. Yikes! Obviously, too much sugar is not a good thing. But as bakers, we love it and we are interested in how it affects our work, so I'll give you a bit of what I know on that.
White sugar makes a crispier cookie than if you were using brown sugar or liquid sweetener because it holds less moisture. Brown sugar makes for a chewy, moist cookie with less spread. Depending on the crispiness that you want, use all white, all brown, or a combination of the two when baking. White and brown sugar are swapped on a 1:1 ratio. In bread, white sugar won't hold as much moisture though it's not like it will produce a dry loaf.
The color will be a bit paler when baking with white sugar than brown sugar. Brown sugar's flavor is a bit deeper so sometimes it's nice to use white sugar for a cleaner flavor. The effects and flavor of brown sugar can be mimicked by adding a few tablespoons of molasses for each cup of white sugar.
Molasses can be substituted for sugar at an almost equal ratio. It's not quite as sweet so you may want to use 1 1/4 cups molasses for each cup of sugar. Given the acidity of molasses, you will need to add 1/2 teaspoon of baking soda for each cup of molasses. You’ll also want to reduce the amount of liquid in the recipe by 1/4 cup for each cup of molasses.
Note that molasses actually has a significant amount of some vitamins and minerals in it versus sugars. Of course, only when you're consuming significant amounts of it. The flavor of molasses is really strong so usually a portion of the sugar in a recipe is replaced with molasses, not all of it. But...to each their own!
Honey also has a really pronounced flavor, some honeys more than others. I often use honey in place of sugar in cakes that are made with nuts or when baking with fruits that I think would pair well with a floral taste, such as apricot. If a recipe calls for 1 cup of sugar, I reduce honey to about 3/4 cup and adjust the liquids by 1/4 cup (reduce liquid by 1/4 cup or add 1/4 cup flour). Because honey tends to brown faster than sugar, you may want to reduce the oven temp by 25 degrees.
Pure maple syrup, another relatively nutritious sweetener when it comes to vitamins and minerals, can be substituted for sugar similarly to honey. If it's quite thin, which the pure syrup often is, it requires a greater adjustment of the liquid/dry ratio. A 1/2 cup reduction of liquid or 1/2 cup increase of flour is about right. Maple syrup adds an awesome smoky sweet flavor to foods. I haven't found its flavor to be as pronounced in baked goods as that of honey or molasses.
Corn syrup is called for in baking and cooking at times and sometimes for good reason. Corn syrup is an "invert sugar", which means it prevents sugar crystals from forming when white sugar is melted, then cooled. According to David Lebovitz, corn syrup will keep your caramel smooth and give gloss to your sauce. I never have corn syrup in my pantry, but I do have fake maple syrup which is made with corn syrup, so I use that. Works like a charm!
Disclaimer: I'm no doctor, or a professional expert for that matter. Most of my experimenting in sweetener substitutions is done when I'm making homemade granola and in cakes and quick breads. I haven't made cookies with all of the sugar replaced with honey, molasses or maple syrup, only portions of it. Others have, though, especially those looking for sweeteners with a lower glycemic index. They say agave syrup is good for baking, and it has a very low glycemic index, but I haven't baked with it because it's super expensive! I can say for certain, however, that it makes a delicious margarita.
Enjoy your day!