In general, is it better to complete a graduate degree first before deciding to work? Or is it also advisable to take a leave of absence and work while finish your graduate degree later?
It is difficult to finish a degree and work at the same time. This is especially the case if you have to write a (PhD) thesis. There are a number of obstacles. Firstly, you will have to work on the thesis during the evenings and weekends, which is both tiring and can induce RSI. Secondly, you will have no life and this is depressing. Thirdly, both your work and your PhD thesis will suffer. Fourthly, the time taken to complete the thesis could drag out 6 months or even 1 year, before you get close to finishing it. Under these circumstances, many people simply do not finish their thesis.
It's not impossible, though. I know of a few people who have completed their theses after taking on another job. It requires a lot of discipline.
If you have the luxury of taking a leave of absence from work to study, then I'd advise taking it. Get the degree out of the way in as short a time as possible.