I know fairly little about both, but from what I understand, they both divided up populations into different groups -- the Varna with Priest, Warrior, "Agriculturalists and Merchants", "Laborer and service provider" and the estates with the Church, Nobility, and Peasantry. They both seem to be occupation linked and status linked with limited degrees of flexibility.
Obviously that is very broadstrokes for both and there are some obvious differences (e.g. the impression I have is that the King in say France was separate from the Estates and that the Church was a unified entity, while not all Brahmins were part of a particular unified entity), but they seem, on the surface, very similar to me. Is the difference in the Jati which do not have an analogy in Europe (outside of say ethnic minorities or perhaps groups granted monopolistic privilege over a trade or occupation like some guilds?)?
So why am I wrong? What are the key differences between these social arrangements?
EDIT: I'm fairly sure I am wrong, to be clear, which is why I want to know more.
The core issue here is how flexibility worked and how fluid (not in a marriage, endogamous definition of fluidity, but in how castes could move up and down the economic classes as either a group or as individuals).
The Varna system was, before the British Raj, a fluid and reasonably mobile system with no artificial barriers to said mobility. Essentially, Professions were not hereditary, nor were there any rules limiting marriages within these classes (though each regional grouping evolved an endogamous marriage pattern), or taboos on whom one could eat with (2) or indeed as Al Beruni notes in Al Beruni's India(3), rules against living together in communal lodgings and homes.
To give you but one example of how the caste system worked pre and post British era, I would like to refer you to the movements on the caste hierarchy seen amongst the Nadar castes of Tamil Nadu.
As traced extensively in Rule by Numbers: Governmentality in Colonial India (4), the Nadars were, pre British not a unified trading class as they would become post British -note here, when I say pre and post British, while there have been many British steps to stratify and codify castes, the pivotal moment was the British Caste based census of 1901, headed by one Risley - you can read his thoughts on castes in his work, the People of India (5).
The Nadar caste today are a powerful, united trader caste in Tamil Nadu - they were toddy tappers by trade in the 18th century, yet, as an example of how fluid castes could be pre British era, pockets of Nadars in provinces 100-150 kms away were also powerful landlords and within the Nadar grouping, they adopted mores of the other economically powerful castes (wealth and power determined upper and lower castes, pre British India) while the poorer groups of the Nadars aka the Toddy tappers adopted the mores and conventions of the poorer castes. So within the same caste, across a space of just 100 kms, there was a lot of variation in the socio economic status of the Nadars. There was no uniform "trading Nadar caste" as it would be post say the 1850's and accelerated post 1901. Yet another grouping of Nadars who lived in the Madurai region (a district during the British administration that was roughly the size of say modern Israel) were even more powerful administrators and chieftains of the short lived Nayaka Kingdoms based out of Madurai. So as you can see, in a region roughly the size of modern Greece, you had one major caste grouping, but within which you had a large spread of economic standing. In modern terms, within the Nadar caste you had the lowest castes, upper middle and richest castes. Each of these sub groupings didn't have a uniform cultural system, but simply adapted the mores and conventions of the highest economic group in their region.
This in a nutshell is how caste mobility and fluidity worked. There are many more such examples I could provide, the Konds of Orissa, the Khatris of modern day Haryana, the Vellalars and Mukulothevars of Tamil Nadu on how each caste had a lot of fluidity and mobility driven solely by its socio economic status. Take the Vellalars for instance, they had a storied lineage in the Northern and Southern parts of Tamil Nadu during the Chola and Pandya periods (TN during this period would have been roughly the size of modern France+Belgium+Netherlands combined), acting as governors, administrators and generals. At the same time, in the central parts of TN, they were groups of landed small scale farmers and also groups of landless peasants. Similar to the Nadars, there was no uniform cultural more or segregation of the Vellalar caste, rather each regional grouping adopted the conventions of whatever upwardly mobile class in their region.
You would have also noticed one key point here - professions and lack of barriers thereof. A Nadar or a Vellalar could, pre British be anything from a landless peasant to an administrator in a royal court to a powerful landlord. There are even some, imo extreme theories that all the Tamil castes, including the Brahmins and Kshatriya castes actually are an offshoot of a very early sub division (going back to the pre sangam era) of the original vellalar caste who then sub divided into 5 broad groupings which then over time sub divided more. (6) To summarise though the example of the Nadars pre British era. There existed one broad Nadar caste, within this caste there were multiple groupings, driven by the socio economic status of each grouping. Each grouping was bound to its immediate geography with little to no social cohesion as a whole. However as seen by the rich Nadars, each localised grouping was mobile and could go up and down the economic (not caste) ladder.