I've done both (both at the same time, and alternating) and quit. As above, nicotine is nicotine. Quitting one is no different that quitting the other. Just remember that the withdrawal symptoms will generally increase in intensity from day one to day 3, and then start dropping off from there (very slowly). Of course, this is all very dependent on the individual, but there is a scientific basis to the numbers as that's about how long it takes for nicotine to be mostly removed from your system. In my experience (and I've quit cold turkey numerous times) the first week is really bad, with every week past that being a big improvement. For me - after 3 to 4 months - I was done with any physical cravings. But of course that's where the real work starts - since you'll tend to forget everything that sucked about smoking and only remember the chemical relief you thought it gave you.
One note on chewing in particular: I noticed quitting always made my mouth feel aweful. Hard to describe but you likely know what I mean. Almost like you needed something abrasive pressed up against your gums. I found that chewing sunflower seeds really helped with this.