In a shiyur of sofrim here [in Yerushalayim], this interesting subject came up:
What is the correct position of placing the parshiyos shel rosh in their batim?
It says in SA [Rema] 32:46 that the parshiyos should stand in their bayis and the end of glilas ha'klaf [side of shma, ie where it opens to start reading] should face the "kore" [the one reading the parsha, a person standing facing opposite the maineach – one who puts them on his head], so on opening the parsha he could start reading from its begining, shma .. va'ydaber ..
Thus the opening is towards the right side of the kore, ie the kadesh parsha [end of glilas haklaf] is positioned towards the shin wall of the bayis, and not towards the inner wall, and so all 4 parshiyos their opening faces right.
In SA 32:32 "there is no need to add klaf at begining or end of the parshiyos" [ie, not like sefer tora & megila that additional klaf must be left before the begining of the writing "k'day lagol hiekef" [so as to surround the csav part], this is unneeded in tefilin – the csav can start immediately at begining of the klaf and finish at end, the only minimum klaf needed is for hekef gvil, which is minimal.
But there are some rishonim (see Tikun Tefilin Baruch Sh'amar p. 169) that demand klaf empty as to surround the parsha in tefilin as well. This opinion although not hallacha is quoted in MB 32:142 (ויש מחמירין דלכתחלה צריך בתחלה כדי לגול כל הפרשה כמו מזוזה). The emphasis "as mezuza" is to show the source, just as by mezuza empty klaf "k'day lagol hiekef" should be left, so in tefilin.
In regard to mezuza, the SA YD 288:1 that empty klaf should be left. The acharonim debate the issue [see Pishei Teshuva YD there, Keset Hasofer & Lishka 27:1], because this additional klaf "k'day lagol hiekef" will cover the Shaday on the outer side of the mezuza, which is supposed to be seen.
The minhag was not to add klaf, neither to mezuzas or tefilin. But some machamirim do add klaf, both in mezuzos and tefilin.
According to the minhag not to add klaf, both the mezuza and parshiyos resemble, the opening is facing the kore, in tefilin it is a person standing opposite the maneach (as exp. above) and in mezuza the opening is facing a person standing in the doorway, so he can see the shaday which is exactly under the shma, the beginning of the klaf when opened. This is in according to the law (SA YD 289:6) that the shma should be facing outward, towards the doorway.
But according to the machamirim what is the correct procedure?
In mezuza if the klaf kday lagol would wrap exactly once around the csav, it woudn't make a difference because the opening of the klaf is where the shaday and shma are, but what happens if the klaf kday lagol is more or less, so now the opening if facing the 'kore' is not where the shma and shaday are facing!
It is pashut that the hallacha [SA 289 above] requires that the shma faces the person standing in the doorway, so if the opening is not fitting the begining of the csav, the mezuza should be positioned according to the shma & shaday, not according to the opening.
And what about parshiyos? In the parshiyos there is no requirement of shma facing the house/doorway, so the lashon of Rema 32:46 [quote above] teaches that the opening of the klaf no matter how long and which way after wrapped the shma will face, is to the right – so that the kore when opening the klaf can start reading.
So there is a slight difference in this issue between mezuza and parshiyos.