Assuming the two answers are in disagreement, a nafka minah would be whether someone who comes home after the time of tichleh regel min hashuk can light. According to the first answer, ad she’tichleh regel is a time limit; according to the second answer, it’s just a shiur in how much oil you need. Tosfos paskens that since the issue is a machlokes, you can light late m’safeik, while the Rambam disagrees.
Shulchan Aruch (672:2) ruless that l’chatchila one should try to light on time in consideration for the Rambam’s view, but b’dieved one can rely on the view of Tos and light all night.
The Be’er Heitev (based on MG”A) points out that the S.A. seems to omit an important qualification. Since lighting later involves a sfeika d’dina, it would seem that you should light without a bracha. Yet, the S.A. just says that if you are late, b’dieved you can light -– no word aboutthe bracha (see M.B. is Sha’ar haTziyun). Why does the mechabeir omit this important detail?
R’ Ya’akov Emden answers that there is a difference between brachos on ner Chanukah and all other brachos. If you just light a candle, esp if you in chutz la’aretz where we light indoors, the only thing that distinguishes what you are doing as being l’shem mitzvah as opposed to just wanting to have light in the room is the fact that you recite brachos on the hadlakah. Unlike the bracha on shofar, or the bracha on lulav,where it is clear what the cheftza shel mitzvah is and the bracha is just added icing on the cake, when it comes to ner chanukah it is the bracha that defines the ner as a cheftza shel mitzvah. It is therefore part and parcel of the hadlakah itself. Whenever you do a hadlakah, even m’safeik, the brachos must be part of the ma'aseh mitzvah.