Why do some Buddhists regard nirvana as an important goal while other want better rebirth?
Do all Buddhists have the same goal and if not why?
Traditional Mahayana answer is: because of different "capacities". People of "lower capacity" only care about fulfilling basic desires, perhaps just the animal instincts, - then going up the ladder we get those that want material happiness in this world (e.g. comfortable family life), then those who aspire to greater immaterial (but still this-worldly) achievements and realizations, and then those who aspire to rebirth in a better world.
Then we get to the next level, that of spiritual practitioners, who aspire to find the truth, become saints, attain supernatural abilities etc. like e.g. immortality, then those who strive for Enlightenment/Nirvana (this is considered the middling capacity) - and then, according to Mahayana, the higher capacity, which entails desire to attain Enlightenment in order to help all the rest of sentient beings. Finally, in Vajrayana, we get to people of "highest capacity" who directly see Great Perfection of Everything As Is and do not have any goals or desires.
This is the traditional answer (retold in casual simplification). Now if you ask my personal opinion, I would beg you to notice that all these goals are not really in logical opposition with each other. If you think about it, all goals represent various visions of Happiness, or "The Way Things Should Be" - as it appears to each respective type of person. It's not that the lower levels are wrong about their idea of happiness, it's just that they don't quite realize how much hidden suffering is inherent to success on each of the levels.
So really what Buddhism is after, is realization of one's highest aspirations. And on every level of this pyramid Buddha-Dharma provides very rational, methodical, consistent framework for achieving success. What makes Buddhism cool though, is that the practices for achieving success on every level are not just in no conflict with other levels but actually help the levels above and below it.
For example, if one practices emotional intelligence, one will not only have greater control over events of one's life, but also become able to help others still overwhelmed by stress, and also get a step closer to Enlightenment through understanding the nature of mind-made phenomena.
So, to summarize, it seems like Buddhism has multiple goals - but that's just the way it looks from the perspective of different individuals. In reality there is One Goal ("peace"/"happiness"), and Buddhism is the rational method for achieving it.
I think there are traditionally two. In one of the suttas (MN 117), the Buddha said,
"And what is right view? Right view, I tell you, is of two sorts: There is right view with effluents, siding with merit, resulting in acquisitions [of becoming]; there is right view that is noble, without effluents, transcendent, a factor of the path.
"And what is the right view with effluents, siding with merit, resulting in acquisitions? 'There is what is given, what is offered, what is sacrificed. There are fruits & results of good & bad actions. There is this world & the next world. There is mother & father. There are spontaneously reborn beings; there are contemplatives & brahmans who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.' This is the right view with effluents, siding with merit, resulting in acquisitions.
"And what is the right view that is noble, without effluents, transcendent, a factor of the path? The discernment, the faculty of discernment, the strength of discernment, analysis of qualities as a factor for awakening, the path factor of right view in one developing the noble path whose mind is noble, whose mind is without effluents, who is fully possessed of the noble path. This is the right view that is noble, without effluents, transcendent, a factor of the path.
If I can summarise I think that the first type of right view is that there are good and bad actions which result in further becoming and acquisitions; contrasted with the second type of right view.
Each of these words (effluent, merit, and so on) can be (has been) a topic of its own.
The simplest (shortest) summary of what the Buddha taught is maybe "Both formerly & now, it is only stress that I describe, and the cessation of stress." The next step up from that in complexity (or rather, the same doctrine but in more detail -- also the first sutta that he spoke) is the doctrine[s] of the Middle Way and Four Noble Truths.
However various schools may have different views: about what nirvana is, about continuing existence in samsara, about the role of the Buddha (as saviour) versus one's own responsibility.
Incidentally I think that another Buddhist doctrine is that people are confused about what they want, what they ought to want, whether what they want is satisfying and/or right, and so on. I think this (confusion) is part of what's meant by "ignorance" as one of the fundamental drivers of the wheel of life. I mention that because your question ("What do Buddhists want?") might include an assumption ("Buddhists are wise and want the right thing. I too should want what Buddhists want.").
Nirvana is the ending of rebirth therefore the two goals are completely antagonist. Rebirth is for what Buddhism calls 'ordinary people' ('puthujjana'). All beings are born into the world with reproductive instincts & only a few freaks are able to attain Nirvana. Nirvana is for people who are genuinely disenchanted with the world & sex. For the puthajjana, Buddhism teaches kamma & rebirth so the puthajjana don't engage in self-harm due to their ignorance.
This answer base on the most ancient theravāda view from the most ancient tipitaka-pāli, that nibbāna is only the best goal, and every rebirth is bad, also every teaching for rebirth is not the best, too.
According to ChrisW answer in this topic:
Life is clinging-aggregates' rebirth. Aggregates' rebirth are paṭiccasamuppāda.
"Now what is the noble truth of stress? Birth is stressful, aging is stressful, death is stressful; sorrow, lamentation, pain, distress, & despair are stressful; association with the unbeloved is stressful; separation from the loved is stressful; not getting what one wants is stressful. In short, the five clinging-aggregates are stressful.
"And what is dependent co-arising? From ignorance as a requisite condition come fabrications. From fabrications as a requisite condition comes consciousness. From consciousness as a requisite condition comes name-&-form. From name-&-form as a requisite condition come the six sense media. From the six sense media as a requisite condition comes contact. From contact as a requisite condition comes feeling. From feeling as a requisite condition comes craving. From craving as a requisite condition comes clinging/sustenance. From clinging/sustenance as a requisite condition comes becoming. From becoming as a requisite condition comes birth. From birth as a requisite condition, then aging & death, sorrow, lamentation, pain, distress, & despair come into play. Such is the origination of this entire mass of stress & suffering.
sāsavā puññabhāgiyā upadhivepakkā
effluents, be merit, giving resultant.
- [saṅkhāra, kamma-bhava] right view that kilesa-vaṭṭa-paṭiccasamuppāda depending on [kāma-āsava (kāma-upādāna), diṭṭhi-āsava (diṭṭhi-upādāna, sīlabata-upādāna), bhava-āsava (attavāda-upādāna), avijjā-āsava],
- right view that is kammavaṭṭa-paṭiccasamuppāda,
- right view that give vipākavaṭṭa-paṭiccasamuppāda.
So, clinging-aggregates' rebirth are paṭiccasamuppāda. And paṭiccasamuppāda are effluents, be merit, giving resultant.
The reasons is answered in S.N. Nidānavagga, which teaching just paṭiccasamuppāda-sutta in various ways. For the example:
Staying at Savatthi. Then the Blessed One, picking up a little bit of dust with the tip of his fingernail, said to the monks, "What do you think, monks? Which is greater: the little bit of dust I have picked up with the tip of my fingernail, or the great earth?"
"The great earth is far greater, lord. The little bit of dust the Blessed One has picked up with the tip of his fingernail is next to nothing. It doesn't even count. It's no comparison. It's not even a fraction, this little bit of dust the Blessed One has picked up with the tip of his fingernail, when compared with the great earth.
"In the same way, monks, few are the beings reborn among human beings. Far more are those reborn elsewhere. Thus you should train yourselves: 'We will live heedfully.' That's how you should train yourselves."
The Buddha's teachings, when properly practiced, all take the practitioner in the direction of Nirvana. The Buddha gave each person the best possible teaching to aim them towards Nirvana based on their previous karma so it wasn't always possible for every individual to make it to total liberation without going through further rebirths.
I don't know if the Buddha ever taught a bodhisattva but that wouldn't make the bodhisattva goal invalid because obviously that was the Buddha's goal.