Are people still fighting about this or have they come to a consensus? Also, as of today (Sep 2015), what is the main advantage of Ripple over Bitcoin?
According to Ripple: Ripple for Financial Institutions Financial institutions, network operators and regulators play critical roles scaling and providing stability to payment systems. Ripple enhances the existing payment stack, offering real-time settlement infrastructure at the foundation."
Given that financial institutions, network operators and especially "regulators" are part of this equation then in this instance of "Financial Institutions" when considering the totality of human involvement it perhaps could not be considered decentralized, which in the context described makes it centralized.
Ripple also states "Jurisdiction or network specific rules, governance, standards, and other critical functions are intended to be provided by existing systems and operators."
With respect to your second question Ripple is a system for exchanging the Internet of Value (many different assets digital and physical) in which they also offer their own XRP digital "currency", whereas Bitcoin is simply another digital currency.
I think this is pretty accurate about Ripple. They are more centralized because of all the regulations they are complying with in order to combat anti money laundering and other know your customer type of compliance. Also, if you look at their advisory board it is composed of many in previous government positions and this will contribute to their centralized aspect of work. Big companies that play by Wall Street rules and are in bed with government to some extent are also within some of the investors of this new institutional digital currency. But even with this Ripple will bring much benefit to average consumers as well and not just the big players.
Are people still fighting about this or have they come to a consensus?
I'm probably the worst person to represent whether there's a consensus or not since I'm one of the designers of Ripple. But the important thing, at least in my opinion, is that there is no "secret sauce".
The software is open source. People are free to modify it however they please. We run the exact same software that we make available on our public servers and our validators. Others are free to run validators and they do so.
As it happens, much of the network infrastructure is run by us today. But we are more than happy to turn that over to others who are willing to do it.
Why do you care if something is decentralized? The main reason is usually that you don't want the users of the system to be forced to accept changes made by an owner/operator of the system whose interest may be averse to them. Ripple is decentralized in this sense.
For example, eBay is not decentralized. They don't warehouse their goods. But if eBay the company says no auctions of adult merchandise, then there will be no such auctions. It wouldn't matter if every user disagreed with the policy. Their only recourse would be to re-create what eBay had done, that is, to themselves implement eBay's secret sauce.
By contrast, Ripple has no secret sauce. Anyone can run their own servers. If we make changes people don't like, nothing requires them to run the code with those changes. If Ripple disappeared and users of the ledger wanted it to continue, nothing would stop them from continuing it.
Also, as of today (Sep 2015), what is the main advantage of Ripple over Bitcoin?
Ripple is aimed at solving different problems from those Bitcoin is trying to solve. Bitcoin is a store of value that includes a payment system for that store of value. Originally, Ripple was aimed at providing a decentralized exchange of arbitrary assets. Today, Ripple is aimed at providing high-speed, low-cost payments between different currencies and even different payment systems.
If you're going to compare them directly (which I don't think is quite the right comparison), I'd say the main advantage of Ripple over Bitcoin is that Ripple's public ledger system natively supports cross-currency payments using a system of order books. Because these order books operate using open source software with all the inputs coming from a public block chain, there is minimal risk of unfair order execution.
Also, there is almost no barrier to entry. For less than $1 worth of XRP, you can create your own asset and people can place offers to buy and sell this asset for any other asset on the public ledger.
Does Ripple operate on a Private Blockchain then? If so, This makes it completely decentralised since only a limited amount of known nodes can participate in the validation process. This goes against the whole concept of cryptocurrency, because it essentially makes Ripple an intermediary that validates transactions between me and you