For the most part if you want to do development economics AND plan to pursue a PhD in economics, then you probably should study for a masters in economics and select development economics as one of your electives. The program you mentioned at LSE is a policy program so if you plan to apply to PhD policy programs, then that might be the better fit. Think also about class size and the number of students in each program. Try to find out where previous masters students from each program have gone after completing the degree. This will probably give you the best answer to your question. Consider reaching out to the different programs to get the answers that you want. In terms of getting a job directly out of the masters program, LSE is probably the way to go.