Were they seen as enemies, potential trading partners, allies (considering the Safavids were enemies of the Ottomans) or just ignored? Are there any documents/accounts from European explorers/traders about them?
There was certainly contact between the European powers and both Mughal India and Safavid Iran. This period was the beginning of the European colonisation of Asia so most of the time relations were built on the foundation of trade and to protect certain outposts (or factories) established by these colonisers who were mainly, for the most part, interested in trade. The only religious effort was in relation to Mughal India where Jesuits under Portuguese dominion came and tried to convert, they were successful in Goa, but failed to gain a foothold anywhere else. Some of the times there were battles but this was also only against the Portuguese and there aren't any conflicts with regards to the British or French at least as far as I can recall.
The Portuguese had reached Mughal India prior to the beginning of the reign of Akbar (1556-1605 CE) and had established relations with them when the Mughals conquered Gujarat. Relations with them were frosty at best due to the fact that they controlled the sea passage routes in the Arabic and Indian ocean and often the Mughal emperor had to ask them to provide passages of safety for ships that were departing on the Hajj. They often used the Ottomans to help them defend against Portuguese aggression on the seas.
Later on the British gain prominence during the reign of Akbar's successor Jahangir (1605-1627 CE). The most famous of the British explorer was Thomas Roe who was there to negotiate protection for the East India Company.
There are a number of diaries written by explorers and diplomats but I only know of French and British ones.
There were also accounts written by the Mughal Emperors themselves which can be found in their biographies.