Hi Kate,
The only reason why I hesitated in answering your question is that I have no personal experience with the Dermawand. I do use the NuFace Trinity though. Here goes, anyway. 
They are two completely different at-home skincare tools that use two different technologies. Dermawand is Radio Frequency used to tighten and rejuvenate the skin. NuFace is Microcurrent used to tone the skin and re-train facial muscles. Both help with collagen production differently - Dermawand with radio-wave created heat, NuFace with tiny electrical currents; both forms can be complimentary to each other.
In deciding between the two, it depends on what your skincare goals are.
On doing a quick search, an Esthetician in Georgia offers both treatments and gives good descriptions of Radio Frequency and Microcurrent on her website. http://yharper.massagetherapy.com/microcurrent--radio-frequency
On a side note: The term "microcurrent" is used quite freely in the selling of at-home skincare tools because it's hot and trendy. TRUE Microcurrent will not cause facial muscles to contract or twitch. NuFace and Isomers Nutritone are true Microcurrent. Suzanne Somers' Facemaster and Serious Skincare's Egg are not microcurrent, but technically Faradic.
HTH and is not too confusing! Happy New Year!
-J