What is the difference between sociolinguistics and anthropological linguistics? Is there more to it than the research methods (sociolinguistics being more survey and statistics focused, anthropological linguistics being more fieldwork and direct observation focused)?
As the terms are currently used, you're right about the distinction about the methods used. Some other differences are that sociolinguistics typically works more in urban environments and linguistic anthropology typically with smaller communities; linguistic anthropology looks more to other branches of anthropology (especially cultural anthropology) whereas sociolinguistics traditionally tackles more linguisticky questions, especially those motivated by the study of sound change; sociolinguists tend to know and care more about linguistic forms (particularly phonology) whereas linguistic anthropologists care more about social meaning; and so on.
However, sociolinguistics has historically been used in a broader sense, with different traditions sharing publishing in the same edited volumes (Duranti 2003). It was only around the 1980s thatthe word sociolinguistics narrowed to refer to variationist work done in linguistics departments, with linguistic anthropology referring to more anthropological approaches. Moreover, since the second wave (Eckert 2012) of variationist studies, there have been more ethnographic work done in variationist sociolinguistics. There is also increasing convergence between variationist sociolinguistics and linguistic anthropology that draws on tools from both traditions. Bucholtz and Hall (2008) write that
As the history of sociolinguistics and linguistic anthropology shows, a sharp distinction between these fields and others concerned with the sociocultural investigation of language is untenable given their significant common ground.
Bucholtz, Mary & Kira Hall. 2008. All of the above: New coalitions in sociocultural linguistics. Journal of Sociolinguistics 12(4). 401–431.
Duranti, Alessandro. 2003. Language as culture in U.S. anthropology. Current Anthropology 44(3). 323–345.
Eckert, Penelope. 2012. Three waves of variation study: The emergence of meaning in the study of sociolinguistic variation. Annual Review of Anthropology 41. 87–10.