The exporter preview that you are reffering to, sets default lights definition. Once declared (from the awd definition), like in Away3D, the materials are just diffuse with no lights. The player code assign one or more light once added to scene.
The awd file on itself does not hold light information at this state (specs 2.0). So when you load your project, unless you specifically assign lights, they will be displayed with no lighting. flat. Unlike in a controled environement such as your editor where lights are set to give you a better sens of volumes, away3d has no idea that you actually want to set lights. There are tons or cases where you do not need them. Even if an awd2 would hold light information, that does not even say you would want to use them.
For instance, imagine if a designer would create, sell a 3D model in a the awd format and add lights to make it look good so you buy it. Now in your scenery, you have already lights simulating another mood/daytime. Adding the file lights by default would certainly conflict with the ambiance that you try to create. You would even be forced to code some clean up routine to kill lights that you do not even need.
Your second remark is actually similar to the lights. The player probably has an antialiasing value set by default in its code, simply because the dev behind it decided that most projects do need AA. Away3D again, will not apply AA by default because you might not want to. For instance, if you dev for mobile, where AA is unsupported (on exception of few hardwares), you want during development to be able to see the exact same result on desktop as on the device.
Your project probably doesn’t have AA set, that’s why the shape is being “jigsaw” drawn, especially noticable on small viewports sizes such as the picts that you posted.