Mostly upon what you regard as "significant".
You can spend a small fortune in an almost infinite number of ways to obtain an almost infinite number of differences. Which, if any of these differences are significant will vary from person to person.
You have decent mics, and decent interface. Inches of variation in mic placement will produce much bigger sonic differences than changing either of those.
Are you looking to change something for a reason or is it just a matter of curiosity?
You're right in your conclusion, btw, and I'd suggest that you've got the kit balance about right. Your mics are amongst the best available (personal preferences may vary but they're great mics), and your interface offers a very good balance of features, sound quality and price. Ok, there are definitely technically better interfaces which, in an A/B comparison with the 6i6 could produce technically/audibly 'better' results but, taken in isolation, if you can't produce an excellent recording with the 6i6 then it's very unlikely to be the interface's fault. You could pay a little or a lot to get a difference but your present interface isn't likely to be a a significant limiting factor in the quality you can achieve. If I were in your position I'd worry more about getting as much experience as possible with my existing setup before I'd bother with changing anything. With more experience you'll be better placed to judge whether any 'problem' you hear is consistent and due to a particular piece of kit or just a changing personal preference.
There's a lot of bobbins talked online, particularly about preamps, and they're often ascribed magical properties to which they simply can't live up. My feeling is that unless you have the funds to indulge a bit of gas, so long as the preamps you have to use aren't actually significantly degrading the signal, or imposing a strong sonic character that's against your prefernces there are so many more important things affecting sound quality than what preamp you choose. Same goes for converters, etc.. It's nice to be able to spend the money needed to optimise (to your tastes) each stage of a signal chain but the law of diminishing returns applies with a vengeance and it's very easy to spend far too much obsessing over really insignificant changes. Also, how different bits of kit perform usually depends heavily upon how they're used and the context of the rig surrounding them. (Check out the preamp comparison
article on this site (which was done by people who know how to produce a valid comparison) and the followup article and threads on the forum. )
However do try other things when the opportunity presents itself (preferably without it costing you anything) - you might find another interface/preamp/AD/whatever that really stands out for you as an obvious improvement but be aware that differences are very beguiling and it's easy to spend a load of time and money jumping from one setup to another every time you hear something new and interesting. That way madness lies. Not to mention an empty bank balance! And trust your ears more than internet opinions ('specially mine!) and random forum sonic comparisons, many of which are flawed and produced by people who don't even realise why they're flawed. Definitely don't spend money or doubt your ability to hear on the basis of the opinions of people you don't know and trust, no matter how many posts they have on a given forum.
Enjoy the kit you have without worrying about it until you know what, if anything, it's doing that you don't like.