If it had to be once a month I wouldn't do either... To begin with. When you start out with a chiropractor you'll want to do weekly then after a month bi weekly, then monthly. Now massage I find only ever gives consistent results if you go all the time. It feels great sure, but I'm assuming you're looking to get a medical class benefit out of it.
I was in a terrible car accident, and I did the massages for a while. It always helped symptoms but never seemed to fix problems. I felt slightly more like the chiropractor did fix things. Although in my case I was unable to work out for like 2 years due to reinjury of the effected joints. Now that I'm back in it I've found the chiropractor is good to go to if I feel like I need a crack, but if injury seems to have occurred again in the back or knee I actually try the massages first, then follow up a few of them with one chiropractor visit.
Yes my chiro has helped me with knee issues, and he also does the infrared laser + specific deep tissue massage on the area he works with. I think going to a minimal force chiro who puts good stock in muscle work before he/she does thier bit is a must. The ones who just jump on your back can hurt you more.
Also chiro will hurt after the first few times, this is normal. Things are trying to slip back into the wrong place, the spot he/she just attempted to create space in. So some pinching of nerves can be common.
I've done acupuncture, deep tissue, chiro, and pain management. I think unless your really hurt up bad the chiro + massage is the way to go.
Any chance you could afford both for a month or so until you can go into maintenance phase with them??