The short answer is, yes, conversion builds a brand-new database, using the old database as a base.
The longer answer is, "better" is a somewhat subjective question.
Personally, my position is that it's usually better to get rid of extraneous junk at the earliest opportunity. However, there are often good reasons to wait until after conversion. For example, it may be good to keep deprecated scripts around until the customer has had a chance to play with the converted solution and make sure he really doesn't want those old features. Or the new environment may provide features that make it easier to organize the old junk in a way that makes it more obvious what's good to keep around for a release or two more.
In other words, to my knowledge, there's no real technical reason driving a before or after choice. It's largely a matter of your preference.
Really depends if you want to do the clean up now or later. I suggest cleaning it up before and making sure it all works well so you have known clean and good copy BEFORE conversion so then you only have to troubleshoot any conversions issuses you may run into and if the conversion doesn't go well and you need to stay on 11 for some reason you have good clean copy to keep using. As Mike said though the conversion doesn't clean up things for you but there is no technical reason not to clean it up afterwards in 12. Good luck!
I agree with the general opinion taht deleting the junk first is best. This includes unused layouts, if any. Because of the way that FM12 rebuilds a file when converting from earlier versions, it is going to create a bunch of code based on all the stuff it has to replicate. Removing the junk after conversion may not remove all of the file code which FM12 had to add to the new file to recreate that stuff in the first place. One report from DevCon indicated that removing layouts, for instance, does not necessarily remove all the CSS created in support of that layout.
So, it sounds like your final FMP12 files may be smaller if you clean up before conversion than if you clean out the same stuff after conversion.