It's a normal side-effect of switching: you're used to folder (= directories) as your primary means to sort stuff. And you have a large existing directory structure.
Before you do anything with a new app you don't yet fully understand: back up all your photos and don't touch the backup while playing with the app you're trying.
Apps like Aperture and Lightroom work differently from Acdsee: they don't just `folders of images' or so. You have to import them. The three apps are pro apps, so they are more complicated at the expense of being more complex. Depending on the app, this happens in different ways:
(1) Traditional app à la iView Media Pro just catalog stuff. You can drag in top-level directories and the whole directory structure is loaded.
(2) You can tell Lightroom to copy the photos or leave them where they are (referenced), to import them into a single folder or keep the directory structure.
(3) Aperture expects you to import one project at a time. Subfolders subfolders of that project until -- at the last level -- you get albums that contain the actual pictures. I would create the lowest-level directories in Aperture myself (they are written into a separate library file), in my case [year] > [year.month] and then choose `import from folder' to import your folders from there. The directory structure is then maintained within that particular project. For instance, I would create a folder 2009, a subfolder 2009.03 for March this year and then import all subfolders of your March 2009 folder within your directory structure.
You should import in smaller bits anyway, not only because this makes it easier to maintain your old structure, but also because in most cases, apps will choke or crash if you try to import 20,000 photos in one go!
Aperture- and Lightroom-like apps are inherently more powerful (read: a lot more powerful) than Acdsee. If you don't learn the basics, you will not be able to use them properly. The more modern apps will require you to abstract from the file-folder structure only (albums, smart albums, web pages, etc. etc.).
However, there is no use trying to use an app when you do not want to learn how this new app works. Just keep in mind that simpler apps (e. g. Picasa) will not give you the same options pro apps do.