well, the meaning is different, you would say this one if I meet you in the parking and if I ask you where you were before. then "evden geliyoruz" is logical and "evden gidiyoruz" makes no sense, also in English :D
in general we would use "çıkmak" for "going from" ("evden çıkıyoruz" is ideal, evden gidiyoruz is a bit weird). But you can say for example "buradan gidiyoruz" (we are going (away) from here/ we are leaving)
I wrote you this a few days ago, but here is a reminder. :)
"home" normally does not take articles. It is a very special word in English. If you use an article, it is actually another word for a rehabilitation center. That is a totally different word in Turkish.