As pointed out already above, this is not an "either or" situation. Unlike browser based programs, you choose which files to add to the LR catalog. The real power of LR4 as an image asset manager comes into play when you use the Filter bar to search for images in the catalog. Once you get into the habit of entering descriptive keyword information each time you import new photos, you will be able to search your archive more easily and more quickly than compared to a browser, file based system. Once you start to handle thousands of photographs, you may struggle to search through a hierarchical folder management system unless you know precisely in which folder they are stored.
Of course if you have relatively few photographs, then it is not an issue.
PSE11 is an excellent program and does most all of what the amateur requires for manipulating the image. However successive image adjustments in PS progressively degrade the image, whereas LR allows as many adjustments and changes as you wish, but only applies them as a single adjustment when you choose to edit in PS or export as a fixed-pixel image.
Once your photos are in LR, you have all the controls you need to carry out image edit selections, group and rename and make advanced Develop adjustments. When you're ready to take your photos into PS you can easily use the "Photo-Edit in APS" command.
As I don't need to photoshop every image I shoot, it follows that LR4 will be called on first to at least add the images into the catalog, so it will naturally be the most used.