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When fighting with blades remember the shape and weight of the blade tells you what it is made best for. Blades with most of their weight at the base or in the handle are made for accuracy and are best for stabbing. Blades with most of their weight at their tip are made for power and are best for chopping. Blades with their weight spread out evenly can do a bit of everything but not as good as the others, their best for a mix of speed, power, and accuracy.

Straight edged blades are mostly used to thrusting and if you want to cut with them you have to pull or push the blade along its edge to deepen the cut. But curved blades are mostly used to slash and shape of the blade itself cuts for you as the curve of the blade makes a pressure point along the edge for you.

To help give a better understanding of what this means I'll list some blades that are good examples of each blade type.

Rapiers are long and slender swords with most of their weight at the base of the blade. Rapiers are made for speed and accuracy. Best used for thrusting.

Scimitars and scythes are curved blades with most of the wight at the tip of the blade. Scimitars cutting edge are convex while scythes cutting edge are concave. The weight of the blade adds momentum and curve of the blade focuses the energy of the swing on the edge. They are made for power and best for chopping. Also note that concave blades will cut their own path out of a body if you use them to stab. (Side note: you don't need to be really accurate with these blades, as it really easy to cut off body parts with these blades.)

Katanas are one of the few well-balanced swords. Balanced blades are all around tools and can be uses for anything, but the downside is that they don't do any one job all that well. So it is really up the skill of the person using the blade to bring out the best in it. Balanced blades can also be used as projectiles because their flight path tend to be stable.

you probably mean flanged maces like that one:
http://upload.wikimedia.org/wikipedia/commons/2/2d/Buzdygan.jpg
when you look at it closely you will see that there are no blades on it. There are also other models like
http://upload.wikimedia.org/wikipedia/de/5/50/Streitkolben.jpg
that look more like a mace.

Those flanged parts have the same function as the spikes on the morningstar, to vastly increase the preasure put on the part of the enemy where it hits thus even being able to penetrate some plates and put so much pressure on chain that breaking bones was easily done.

To me those seem more like a crossover between a simple mace (any stick whose hitting end got way more weight than it's handle end) and a war hammer. The advantage over the hammer is that it got more sweetspots (i hope that's the right term) to hit the enemy with, the advantage over the morning star would be that the flanges won't bend as easily as spikes when missing the target and e.g. hitting the castle wall and that a morningstar would often hit with more than one spike (which in that case would be slightly offangled to the impact vector). The disadvantage against the hammer would be lower penetration force. There is also the cost factor, making and repairing good durable flanges would require more afford than doing that for the spikes of a morningstar. The advantage over an axe would probably be that an inaccurate hit will still transfer a lot of force to the target, while an inaccurate axe hit may slide of from plate or chain.

edit:
you may also want to take a look at this page
http://otlichnik.tripod.com/medmace3.html