Image service is a type of service where a raster dataset as published and can be accessed by a client. An image service can be cached or dynamic. In the case of Landscape Layers, as you have noticed, they are dynamic image services (at least those I have previewed). This means that you have access to the symbology settings (so you can change a layer appearance directly in a web application), raster attributes if they were exposed (the ones you can see in the attribute table) and so on. Of course you can consume these layers within your ArcGIS Desktop application, but in either case you would need an AGOL for Organizations account.
The purpose of the image services of Landscape layers is to provide you with a good analysis reference. For instance, since it is a non-cached service, you have access to the rich analysis tools exposed via Image Analysis window in ArcMap. So, whatever you could do with a read-only raster dataset on your computer (mosaic dataset raster functions, time sliding, setting symbology and image analysis), you can do this with dynamic image services.
Feature service is a type of service where a vector dataset is being published and exposed to various clients. So, the file or enterprise geodatabase feature classes are published and can be accessed, queried, and sometimes even edited by web or desktop applications. The difference between image services of Landscape Layers is that you can't edit the image services since it is a raster dataset, but you may apply different raster functions on-the-fly for them in your client (such as ArcMap).
So, image services are for having a good reference map (in case of Landscape Layers, those are non-cached dynamic image services that were published based on geodatabase raster datasets, so you can query them) or for GIS analysis (which you can do both in rich web clients or in ArcMap). Feature services are for accessing and editing vector GIS data and not for publishing rasters.