This is a very broad question that doesn't have a single answer, but I'll bullet point some of the most common explanations that have found consensus among historians of India. Hopefully a historian of Iran can provide the other half of the answer to your question.

• There was never a prolonged attempt at converting the Indian populace, although enemies of the state were occasionally forced to convert. Although Hindu nationalists frequently point out a number of temples were destroyed by Muslim conquerors, almost all were destroyed in the course of war or during a rebellion, and were almost never tied to conversion to Islam. Temple destruction is best understood as a tool used by Muslim (and Hindu) rulers seeking to challenge their political opponents, not as a religious statement (EDIT: changed wording slightly to avoid confusion). As Metcalf and Metcalf put it, the goal of Muslim states in India was to extend Muslim power, not to convert or oppress Hindus. This leads into the second point:
• Muslim rulers in India quickly discovered that the best way to extend Muslim power was to ally with Hindu polities, social groups, rulers, militias, and religious institutions. The most prominent example is no doubt the longstanding alliance between Rajputs and the Mughals (see Jodha Bai's marriage to Emperor Akbar), which solidified the power of both parties for centuries in North India. Indeed, the Mughal state itself was most responsible for the ascendance of several majority Hindu groups that would come to define Hindu power in India (e.g. Marathas, Rajputs, and Jats).
• Even Aurangzeb, notorious among Hindu nationalist historians for his supposed intolerance, patronized Hindu religious institutions and employed Hindus in his administration. For example, a quarter of his mansab holders (basically, men of rank in the military) were Hindu, and most of his wars were waged against Muslim rulers. Aurangzeb is a controversial figure, and I'd be happy to answer more questions about him, but for now I'll move on.
• Although we now understand them as wholly distinct religions, Hinduism and Islam were never fully (EDIT: replaced really with fully for clarity) separate in terms of local practice and traditions. In India, just like every other place where Islam spread to, the religion was incorporated into the existing religious milieu. The lines between Bhakti and Sufi devotionalisms were blurred, and Hindu deities were frequently worshipped by Muslims. As Cynthia Talbot put it, "There is a general consensus that it is questionable whether a Hindu or Muslim identity existed prior to the nineteenth century in any meaningful sense" -- at least at the village level.
• Even educated members of the Mughal court, who knew very well that Islam was distinct in origin from existing indigenous religions, often divided their allegiance between Hindu and Muslim authorities. Most famously, both Akbar and Jahangir were devotees of Hindu yogis and believed that Hinduism and Islam shared a single underlying truth, although a number of prominent Muslim nobles were strongly opposed to such a view, which they deemed heretical.
• Now to answer your other questions. First, you mention that Zoroastrianism was more organized than Hinduism, and that may be true, although I can't say I know much about the history of Zoroastrianism. It is critical to note, however, that it was not just "Hinduism" that managed to survive in India (if such a thing as "Hinduism" even existed at all). Perhaps more crucially, it was Brahmanism (i.e. Brahminical religious institutions) that found a significant foothold in Muslim-ruled India, and later become utterly ascendant under British rule. Brahmins were not particularly well-organized or well-defined before the 17th century, but were patronized extensively by non-Hindu rulers and viewed themselves as representing a distinct religious tradition.
• The last thing you mentioned was Buddhism and Jainism. Buddhism had already long since been on the decline for many centuries by this point, but I'm not sure what you mean when you say that Buddhism and Jainism would make it "easier to convert." Are you suggesting that it was easier to convert from Buddhism or Jainism to Islam than some other religion? I'm not sure if there are any real grounds for such a claim.

Sources:

C. A. Bayly, "The Pre-History of 'Communalism'? Religious Conflict in India, 1700-1860," Modern Asian Studies, 19:2 (1985)

Cynthia Talbot, “Inscribing the Other, Inscribing the Self: Hindu-Muslim Identities in Pre-Colonial India,” Comparative Studies in Society and History 37, no. 4 (1995): 692–722.

Metcalf, Barbara D., and Thomas R. Metcalf. A Concise History of Modern India. Cambridge University Press, 2006.

The first thing I’d say is that Iran didn’t become Islamic overnight. Today we think of Iran as country dominated by conservative Shia Islam, however this only really dates to the 17th century when the Safavid dynasty made Twelver Shi’ism the official religion. The notion of Iran being ruled by a council of clerics only dates back to the 1980s.

For the early Arab conquerors it was a far better option not to convert the Persians. It made the transition to the new regime smoother and opened the population up to paying the jizyah, the Islamic poll tax on non Muslims. It probably wasn’t until after the Abbasid revolution in the 850s CE (200 hundred years after the conquest) the the Muslim population of Iran slipped over 50%. You can see similar patterns in other countries. When the crusaders arrived in Palestine in the 1090s the vast majority of the population was Christian.

With that point out the way let’s look at India. Islam arrived in two different ways: through trade and invasion.

The first Muslim incursions into modern day Pakistan came in the 8th century, establishing Umayyad rule in Sindh, however it really wasn’t until the 11th century that Muslim dynasties made large gains in India. This was done by three successive Turkic states called the Ghaznavids, the Ghorids and the Delihi Sultunate. The first two ended up controlling northern India while the latter ruled most of the subcontinent. All three of these states were conscious of their vulnerability as interlopers and saw no reason to annoy their subject populations by forced conversions. While there were certainly several incidents of religious persecution the Delhi sultans ultimately needed Hindus to make their Empire run smoothly. It should also be pointed out that medieval India’s population numbered in the hundreds of millions. Islam in India took on a distinctively Indian form, and became one more faith in the diverse religious milieu. Merchants spread Islam, especially Sufi Islam far and wide, notably Bengal which today has one of India’s highest Islamic populations but is distant from the historic centres of Muslim power. While many people were converted willingly, Islam had little appeal to high caste Hindus who would loose their social status. A problem that Christian missionaries up to the present day also encounter.

Sufi Islam in its Indian form entered into dialogue with Hindu traditions and became largely pluralistic in its outlook. At the court of India’s last Muslim Empire: The Mughals Islam was seen as one aspect of an eternal truth rather than having a monopoly on it. The Mughal Emperor Akbar removed all restrictions and invited thinkers from all known religions to debate with him. One consequence of this was Akbar’s founding of his own religion: the Din I Ilahi which he intended to contain the truths of all religions.

Even Aurangzeb the notoriously conservative Sunni Mughal Emperor had thousands of Hindu officials in his army and bureaucracy. Aurangzeb probably wished he could convert all of India to Islam. Though even for one of the most powerful people in the world, this was not practical.

Edit: removed short paragraph on Zoroastrianism which requires fact checking.