There are many elements of style, of the narrator voice, that have changed over time. @ChrisSunami talks about this, and brings the example of Jonathan Strange & Mr. Norrel - one example I was going to bring. Let me give you some other examples, with the various effect they produce.
The translation of the Aeneid that I have standing on my shelf is a translation to Hebrew, that has been done using the language and turn of phrase of late 2nd Temple. (Contrary to what some might believe, the language is perfectly accessible. We Jews just have to be an exception to every rule, so we went and preserved a language virtually unchanged for 2000 years.) Such a translation choice sort of makes sense - the Aeneid was written around 20BCE, so translating it to the Hebrew of the day is not a total case of "what were you thinking?!".
While the language was that of 2nd Temple Judea, the style was of course that of Virgil - it was, after all, a translation.
The effect of such a text is not unpleasant, but it is weird. Words and expressions are used in ways they have not been used before - turns of phrase I have only ever seen in the context of one particular prayer, for example, are turned to other uses. The use makes perfect sense, but the weirdness is still there, even towards the end of the epic. At times, it threw me out of the reading entirely, and I stopped to observe the effect the words created. (I do not consider this necessarily a bad thing. But it is a thing that happened.)
This could be an effect you might wish to deliberately invoke. Still, you need to be aware that this is the effect that will be produced if the language you use is too old and context-specific.
A completely different example is The Lord of the Rings. The language Tolkien uses is not particularly antiquated. It doesn't strike you as either "modern" or "old", except when he seeks to invoke a particular effect. What Tolkien takes instead into the story is sensibilities that belong to a medieval ballad rather than a modern novel. He introduces characters, and tells us about them straight away, instead of letting them reveal themselves. The men in his story are "larger than life" in their heroic resolve and feats of arms, the women possess an unearthly beauty. They all act on "callings", not on whims. It could almost be argued that the hobbits are the only real, flesh-and-blood humans there, and they have somehow strayed into an ancient ballad.
Think of style not as one thing, but as a combination of elements. For each element you can decide separately whether, and to what extent, you want to have it "period" or "modern". Various uses of each element are possible, producing different effects.
I would agree with @Amadeus that stepping out of the language-style-sensibilities modern comfort zone would place more demands on the reader, making the reading somewhat "harder". However, I believe it also has the potential of being more rewarding, if you make good use of the tools in your hand. (Consider The Lord of the Rings as an example.)