When so much of life has become globalized, these two terms--sense of place and placelessness--both relate in some way to the renewed focus on place, whether place is considered as the location (or locality) of life in a town or city, or how places/localities relate to the whole world.
Sense of place is the collection of meanings, beliefs, symbols, values, and feelings that individuals or groups associate with a particular locality. With high rates of mobility, increasing tenuousness with the natural environment, increasing mediatization of the lifeworld (TV, computers, cell phones, IM, texting), it is thought that people are losing much of their rootedness to where they live. Thus, they do not have, if this is correct, a deep attachment to place--their sense of place is underdeveloped.
Placelessness, then, has two meanings: Places themselves are increasingly homogenized in a McDonaldization of the landscape (cityscapes with their chain businesses look similar). And, people themselves experience placelessness when living in a placeless, homogenized landscape.
Refer to sense of place above and you can see that the two terms relate in reverse: Sense of place provides identity to individuals and collectives; placelessness occurs when an individual or collective experiences little emotional connection to a place. Sense of place measures attachment and identification to a place; placelessness measures the lack of connection and identification to a place.