The Baal HaTurim asks your question (Gen. 13:14). He explains that Abraham was told the directions starting with the north in order to acknowledge the merit of Abraham's korbanos, which are to be slaughtered in the north (of the Temple courtyard?). Yaakov was told about the west first, in order to let him know that in his merit the sea would split for his descendants. A remez is brought to prove this. The verse says "And Israel saw the mighty hand..." by the splitting of the sea etc. The Baal HaTurim explain the word Israel to refer to Yaakov himself. Later, by Gen. 28:14, The Baal HaTurim continues this explanation by showing that the gematria of "U'faratzta yama" is the same as "krias yam".
The Kli Yakar on Gen. 28:14, explains that it is Yaakov's sequence which is out of order. This is done to provide a remez to reassure Yaakov about the future tribulations of Klal Yisroel. West is the setting sun. This shows that the Jewish people may endure a crushing lowering of status. However, this will bring them to fully trust in Hashem, only; through humility. This will lead to their salvation which will turn the situation East; which is the strength of the new sun dawning. So, even if the Jews will be enduring darkness and a reduced state (represented by the North), they will eventually dwell in great heights. (Dar - Rom) The word South is seen here as a combination of two words "dwell - high". The descendants of Yaakov will eventually be elevated throughout the world. See there at length.
I have been inspired to receive my own vort for you. I hope you like it.
In Gen. 13:14, the exact order of the compass directions, seem to be given to Abraham midah k'neged midah. This measure for measure choice of wording would have the effect of providing approval for Abraham after he just passed another test by sending Lot away.
When Lot was told to please choose a direction, the Torah tells us that he "lifted up his eyes" and saw Soddom. Now if a man lifts up his eyes and sees a place, it must mean that he was facing it to begin with. Therefore, Abraham and Lot were standing facing Soddom (East). Abraham then offered Lot use of a portion of the land he himself was promised, for the sake of peace. First he offered the "Left" and then the "Right" as an alternative. So, he first offers Lot the North, then South. Lot however picks East. Abraham accepts giving up the East. The West was not involved.
Therefore the Torah uses the specific wording that Abraham should also "lift up his eyes" (as Lot did) "from the place in which he was" (referring to that same vantage point where he offered the choice to Lot) and look North, then South, then East, then West (in the same order he offered pieces to Lot). He was then told all of the promised land would be his anyway. This was a heavenly acknowledgement that he had passed the test and handled Lot correctly.
Abraham's intent, was that Lot either pick the North or South of Eretz Yisrael. This is because the Land would keep Lot connected to Hashem because he would constantly need to pray for rain. However, Lot chose straight ahead, since Soddom was like a watered garden (like Egypt) which did not need rain. (see Devarim 11: 10-12)
Yaakov however was about to leave the Holy Land, and was worried about returning intact. Therefore, Hashem wanted to reassure him by starting off with the West. Yakov was heading to the land of the East. So, in order to return, he would need to go West. So too, in any future exile, (Yaakov was shown the 4 exiles at this point) his children were first promised to spread out West which would represent a return to the place of the Shechinah's dwelling, (the Temple in the land of Israel) which is always in the West.
Antoninus asked Rebbi: "Why does the sun rise in the east and set in the west?"
Rebbi: "If it were the opposite you would ask the same thing!"
Ant.: No, I mean why doesn't it just circle back to where it began. Why does it set?"
Rebbi: "In order to give "Shalom"(bow in obedience) to its Creator."
You see from here that the Shechinah (Divine Presence) is in the west. (see Sanhedrin 91b with meforshim.)
Hope this helps. :)