The four Imams and the majority of the Sahaabah and Taabi’een were of the view that fasting whilst traveling is permissible and is correct and valid. If the traveler fasts, it counts and he does not have to make it up. See al-Mawsoo’ah al-Fiqhiyyah, vol. 28, p. 73
As to what is better, that depends:
1 – If fasting and not fasting are the same, in the sense that fasting does not affect him, then in this case fasting is better, because of the following evidence:
(a) It was narrated that Abu’l-Darda’ (may Allaah be pleased with him) said: “We went out with the Messenger of Allaah (peace and blessings of Allaah be upon him) [on a journey] during the month of Ramadaan when it was intensely hot, until one of us would put his hand on his head because of the intense heat, and no one among us was fasting apart from the Messenger of Allaah (peace and blessings of Allaah be upon him) and ‘Abd-Allaah ibn Rawaahah.” (Narrated by al-Bukhaari, 1945; Muslim, no. 1122).
(b) Fasting whilst traveling means that one fulfils one's duty more quickly, because making it up later means delaying it, but fasting in Ramadaan means doing it sooner.
(c) It is usually easier for the one who has this duty, because fasting and breaking the fast with the people is easier than starting to fast all over again.
(d) It makes the most of a blessed time, namely Ramadaan, for Ramadaan is better than other times, because it is the time when fasting is obligatory. Based on this evidence the view of al-Shafaa’i, which is that fasting is better in the case of one for whom fasting and not fasting are the same, is most likely to be correct.
2 – If not fasting is easier for him, then in this case we say that not fasting (when traveling) is better. If something will give him hardship, then in his case fasting becomes makrooh, because doing something that causes hardship when there is a concession indicates that one is spurning a concession granted by Allaah.
3 – If it will case unbearable difficulty, then in this case it becomes haraam for him to fast. The evidence for that is the report narrated by Muslim from Jaabir ibn ‘Abd-Allaah (may Allaah be pleased with them), that the Messenger of Allaah (peace and blessings of Allaah be upon him) went out to Makkah in the year of the Conquest in Ramadaan, and fasted until he reached Kuraa’ al-Ghameem. The people were fasting, but he called for a cup of water and lifted it up so that the people could see it, then he drank it. After that, he was told that some of the people had continued to fast. He said, “Those are the disobedient, those are the disobedient.” According to another report, he was told, “The people are finding it hard to fast, and they are waiting to see what you will do.” So he called for a cup of water after ‘Asr. (1114) So he described those who fasted even though it was very difficult as being disobedient. See al-Sharh al-Mumti’ by Shaykh Muhammad ibn ‘Uthaymeen (may Allaah have mercy on him), vol. 6, p. 355).
Al-Nawawi and al-Kamaal ibn al-Humaam said: the ahaadeeth which indicate that it is better not to fast are to be interpreted as referring to those who will be harmed by fasting; in some of them this is clearly stated, so they must be interpreted in this manner, so as to reconcile between the ahaadeeth. That is better than neglecting some of them or claiming that they have been abrogated, without definitive evidence to that effect. In the case of those for whom fasting and not fasting are the same, they quoted as evidence the hadeeth of ‘Aa’ishah (may Allaah be pleased with her), that Hamzah ibn ‘Amr al-Aslami (may Allaah be pleased with him) said to the Prophet (peace and blessings of Allaah be upon him): “Should I fast whilst traveling?” – and he used to fast a lot. He (the Prophet (peace and blessings of Allaah be upon him)) said: “if you want to, then fast; if you don’t want to, then do not fast.” (Agreed upon).