Either one will do the job, but make sure you buy and use the right ones. If using a comb, don't use the plastic molded ones. The plastic molded combs have seams down the sides that will cause split ends and breakage. Look for specially made combs, that are hand carved and made from metal, wood, bone, horn, and other materials that will not cause breakage. Combs are good on the go, but for home use I recommend a good boar bristle brush. This will distribute the beard oil or beard balm evenly throughout your beard down to your skin, conditioning your skin to prevent dry itchy skin.
It is important to maintain and trim your beard throughout the year. Even if you are planning or growing it forever. At least one a month, I recommend trimming 1/8" off the ends of your beard. This keeps your beard looking fresh and will encourage growth. Start with a damp clean beard. At this point you can start on your left or right and follow through to the other side, a little at a time. No need to hurry, you don't want to cut too much off. If you are worried about cutting to much off or making it uneven, then go see your local barber. They will be more then happy to trim it for you.