Back in the day when I was "new" at this writing thing I would multitask mostly because I would get bored with one story and feel the urge to start writing a completely new story to make writing entertaining again. Also, if I felt inspired to write a certain story I just started writing it. That only worked for a short while before I started becoming stressed about the stories I had. One time I believe I was trying to continue three stories at once just to start two more and then try to work on all those (back in my yahoo group days) and then I got here and wised up. Multitasking is "ok" in short bursts, but trying to continue two large projects at one time can lend to some pretty huge hurdles. Like keeping both of them on some sort of posting schedule, keeping them edited, keeping the plot, characters, setting, and such on track, and etc.
So in my experience, if you want to sustain both stories only work on the story that you feel most inspired in writing. You can on occasion open and read and write on the other projects you may have, but as a new author I wouldn't recommend sustaining two stories. An anthology and a serial is a good way of multitasking, but since you're new bad habits on a grand scale could arise and I would much rather have one learning process instead of two with two different stories.
Do keep both stories don't delete either.
Good luck.