Totally quit both at the same time.
Get the quitting over with once and for all to reduce the bullcrap withdrawls and extending the lousy feelings and cravings over a longer period of time.
the faster you quit smoking the better you will feel, the next day.
for me i could never quit one then the other, and the two go hand in hand so having a smoke could trigger constant booze cravings, some addictions go together, like coffee and cigarettes, you know, in order to help quit smoking some folks have to give up coffee for a while as well.
That's how i have to quit, and if i take up smoking again it always leads back to drinking because for me the two go hand in hand... Refraining from one makes it easer to not do the other....
Some people refer to it as a double quit. and it's not as hard to do as you think. You can do it.
YES you can do it. personally i think it's easer to get the quitting over with once and for all.