I've heard awesome things about Lightroom, I have the program via Adobe Creative Cloud, and as soon as I teach myself some unrelated PHP and WordPress child theme stuff I need to learn, then I will dig into learning LR.
I think you'll like it... but there is a major "rethink" necessary to fully appreciate Lightroom's organizational power. And Aperture, too.
You have to 'let go' of your photos as tangible things. By default Lightroom wants to move your images into a date ordered folder system. Just let it do its thing. However, make sure you take the time to keyword the images as they are imported. Initially, you might just add the same names as the nested folders you are currently using. Also... take the time to create the "Collections" as you go. Think of a Collection as folder (in the nested folder sense) or an Album in iPhoto or Aperture. Collections can be grouped into Collection Sets...
You can then drag photos into the Collection that matches the way you would have set up a nested folder structure. At this point, admittedly, the benefit is hard to see. But wait - there's more!
A photo does physically reside in the Collection...it is merely a pointer. Which means you can have 'pointers' (images) in as many Collections as you want, without increasing the storage needed (since it is just a text pointer that is being duplicated in a database entry). So, for instance.... Your best friend Fred comes over to visit your family for your birthday. Fred brings a rare breed of monkey because he knows you like to take photos of monkeys. You get a photo of Fred, with the monkey and your family at your birthday party... and since you used the self timer, you're in the photo too.
With the old-fashioned nested folder structure, do you file this image under the date? In the 'My Birthday', 'My Family', 'Monkey', 'Friends', or 'Photos of Me' folder? In 3 years when you need to find that photo again because this is the monkey that was wandering around an Ikea store in Toronto and the local paper will pay you for your copy will you remember where filed it?
With Lightroom you can file it under all of those Collections (It is automatically filed by date, so you don't need to do that). Plus if you have added the keywords, you can just do a search on "monkey" and whatever else may narrow that search.
Plus...you have Smart Collections. These are like permanent searches. Going back to our hypothetical example, people know you have lots of photos of Monkeys and are always asking you for a copy. Since you are adding keywords (Monkey & species, perhaps?) as you import you can set up a Smart Collection that updates itself automatically to show you all the photos that have keyword "Monkey" attached. You never have to go looking for them.. you just open a Collection (which is exactly like opening up a folder) to see all the photos. Smart Collections can have very complex filters that narrow searches by more variables than you can shake a stick at.... for instance you can search (or exclude) lense focal lengths, apertures, camera make, etc etc.
And that is just the scratching the surface of the power of Lightroom's organizational power. To be balanced, Aperture has similar abilities as well.
The key is to "let go" of your images. Let Lightroom do what it wants to do. You need to know that Lightroom (and Aperture) never alter your photos - even when you edit them in those applications. All of these things are being recorded in a database. It's why you never "save" and why you don't move your images around outside of the applications. It's also why the space needed can stay pretty modest even if you have lots of variations and duplicates. You can always "reset" an image to go back to the image you initially imported.
Think of it as a public library, where you request a book and it is brought to you at the front desk. The card catalogue is the Lightroom interface. There are multiple records for the same book... one by author, one by publishing date, one by topic, one by publisher. And you never really need to know where the book is... you just say "I want that one, please" and it is fetched for you. Except that Lightroom also gives you the ability to "look" at the books on the shelf next to the one you want. Sometimes you need to "browse" visually... so you use the search features to find the image you know is near the one you have in mind, and then browse.
Once you have gotten used to the basic functioning of Lightroom, it is flexible enough that you can change some of the defaults. But initially, just stick to the default organizing scheme. The Help files assume this is the case, and you find that the default scheme is pretty well thought out.
Hope this helps.