Asked by Samuel,
This essentially comes down to preservation potential of landforms. Eskers underneath ice sheets can be quite large features, filled in with sand and gravel. As a result, after ice-sheet recession, they form fairly robust features that can withstand post-glacial processes of wasting and redeposition. One of the most famous eskers in the UK is the Blakeney Esker in Norfolk.
Lateral moraines are preserved in the landform record, but are often quite subtle features plastered onto hillsides, so are perhaps less obvious than large, prominent terminal moraines. The photograph below is an example of a lateral moraine at Glen Isla in Scotland. The river Isla, close to its source at this point, has cut away at the lateral moraine deposits. From www.Geograph.org.uk.
In contrast, medial moraines are often quite small, superficial features, resulting from supraglacial debris falling onto the glacier. In the photograph below, you can see that one of the medial moraines starts below a rocky outcrop, from rocks falling onto the glacier surface. They are therefore likely to contain less debris, and have less preservation potential, than a terminal moraine that is built up over a longer period of time in one position.
Medial moraines may also form where two glaciers join, but again, although they look striking on the glaciers, they are unlikely to result in pronounced landforms once the glacier melts. Most of the debris will just end up building up at the terminal moraine position.
In the aerial photograph below, you can see medial glacier moraines on the Nuussuaq Peninsula, Greenland. Medial moraines, which form on the glacier surface, may be ice-cored, which makes them seem like they contain more debris than they actually do. From Wikimedia Commons.