It's hard to describe. Well, first they tend to be sharp, and well made ones will cut paper just by dragging it along the edge.
Depends on the sword. If you're sharpening a longsword (or other sword from around the same place and era) the most correct edge is fairly blunt--similar to a chisel edge--for improved durability against the materials you historically would have been cutting. Compared to the edge you'll see on a lot of stainless-steel replicas, it's not particularly impressive; even 440A stainless can be similarly sharp if you use a more knife-like edge. There are also plenty of "in-between" swords (or sword-like objects--I like that term), that are well-made enough to be made of a high-carbon steel, and to hold an edge well, but that aren't actually all that durable or well-made and that I wouldn't call a battle-ready sword. (eg, go on eBay and buy a $200 katana. Some of them are pretty, but I wouldn't trust any of them for durability.)
To me, a more clear differentiation is flexibility. A properly-made sword will bend--a lot--and spring back to its original shape. Most replicas will either bend and stay bent or just break.
There's even a visual difference. A properly-made sword isn't nearly as shiny as a mass-produced stainless-steel replica. Stainless steel has an almost chrome appearance to it... largely because stainless steel contains chromium. A well-polished high-carbon steel can shine, but it looks different. I'd almost call it a different color, but it's really not something I can describe. This leads on to another key difference--rust. Stainless steel swords don't rust--that's the whole point of stainless steel. High-carbon steels do--hold a high-carbon blade in your fingers, sheathe it, and come back in a week and you'll have a nice rust copy of your fingerprint on the blade, and it'll take a hell of a lot of work to get it off. (Ask me how I know.
![Sad](http://saberforum.com/Smileys/default/sad.gif)
) You learn very quickly to take care of your blades!
Also, replicas of fantasy swords
look like fantasy swords. They tend to have lots of fancy-looking extraneous junk. A battle-ready sword tends to be relatively simple in design; simply put, it has a job to do and anything that doesn't work toward accomplishing that job shouldn't be there.
Kinda like how Ultrasabers combat lightsabers feel different and more premium and awesomer then the "other guys" lightsaber wall lamps/movie replica lightsaber even ones Star Wars licensed?
That's actually not a bad comparison. My Force FX ANH Luke feels like somebody made it to look pretty. (...because they did.) My Ultrasabers feel like somebody made them to be used. (...because they did.) There's a similar difference in weight and balance on proper swords vs replicas.
In a nutshell, if you just want a sword to hang on your wall, you actually might be better with a stainless steel replica. They usually look more fancy, they don't rust, and they take nothing more than a bit of dusting to keep looking factory-fresh. Just don't ever try to use them for anything but display!