Partially finished basement needing dehumidification
If you get one larger dehumidifer, it  is generally more energy efficient than two smaller ones running in separate areas as noted by Keshlam. However, it also may not dehumidify both spaces equally depending on air flow. It all depends on the possible products available, the spaces you are planning to condition, and the degree of accuracy you wish to control humidity in both spaces.

If you are running two of the same dehumidifier (buying a second to supplement an existing rather than upsizing to a single more efficient model), then theoretically it could consume the same energy depending on the specs of the dehumidifier (starting the dehumidifiers has an initial spike in energy to get the motors going, so doubling the power required to start two motors instead of one might make two a slightly less efficient configuration, but most likely not enough to make a noticeable impact). However, this isn't a theoretical physics problem with round cows--there are a lot of variables. The cycle times (off/on) could be very short if they are oversized for the space and desired set point--thus shortening the lives of the dehumidifiers and factoring into cost. Or, the cycle times could be very long if undersized for the space--thus shortening the lives of the dehumidifiers and factoring into cost. Basically, as long as you make sure that the dehumidifiers are adequately sized to condition the space (whether you go with one or more), then it shouldn't be too noticeable from a cost of perspective to have multiple dehumidifiers instead of one (apart from the up-front cost of more than one dehumidifier). Also, I'm personally not a huge fan of added fan noise in conditioned spaces like you would get with a second dehumidifier if you're considering that as part of added comfort.