We’re a little limited by our sources in answering this, but at least as it was written, Latin texts of those two periods had some differences, exacerbated by the fact that Latin writing of the archaic period is still in the process of regularizing. We don’t have a huge extant body of early Latin, which adds another layer of complication to things, and a lot of what we do have is transmitted through later sources and there’s no way of knowing how much change happened during that transmission. For point of comparison, the Latin we tend to teach in schools is classical Latin, generally geared toward preparing you for authors like Cicero, Caesar, and Vergil, which makes it a nice mid-point between the two dates you’ve mentioned.

Some of our earliest Latin texts, like the Duenos inscription, date somewhere in the 7th through 5th centuries BCE and whether prose or verse our sources for this period are primarily inscriptions. What we think of as capital-L Latin Literature in the self-aware literary sense of the word doesn’t take off until later. Livy reports an earlier unwritten native Italic dramatic tradition but also writes that “Livius, after some years, was the one who first dared to weave together a play with a plot from the saturae” (Liv. 7.2.8), and tradition gives credit for the origin of Latin literature to Livius Andronicus in 240 BCE. Because we use classical Latin as our default when we teach, when we talk about "archaic Latin" the term can refer to anything from those earliest inscriptions through to early Latin literature, capital L.

That makes for a fairly large time period, and our earliest inscriptions pre-date Andonicus’ first translation of Greek drama for the Ludi Romani by a fair amount. If you learned classical Latin, looking at something like the Duenos inscription for the first time with no previous experience with archaic Latin is utterly baffling and on that measure Latin writing of that period is very, very different. Vowel changes between the two periods, especially for any long vowels or diphthongs, take some getting used to although they are relatively predictable, the differences between c, k, and q aren’t yet regular, and from the classical perspective you have to account for things like rhotacism. On top of that, some early inscriptions are written right to left instead of left to right and there are some that are boustrophedonic (they turn like the plowing of a field), which is another element of later Latin writing that hasn’t been fully regularized yet in the earliest periods. There are a few other things you don’t see in classical Latin, like the future imperatives used in the legal language of the Twelve Tables.

Stylistically, archaic Latin is fairly distinct as well. For anything in verse, Saturnian verse also uses a local Italic qualitative, stress-based meter rather than the quantitative meters adopted from Greek used later. There’s a fair amount of alliteration, repetition, and etymological play, possibly a hold-over from a largely oral culture, especially in religious contexts like the Carmen Saliare. Legal language from the Twelve Tables and the early 2nd century BCE Senatus Consultum de Bacchanalibus has its own distinct style as well.

On the other hand, from classical to archaic Latin is still fundamentally the same language and many of the things changed make written Latin look very, very different from classical Latin but not function any differently. The c/k/q issue is a matter of writing the same sound in different ways and the 2nd century BCE practice of writing lengthened vowels as doubling is a purely orthographic change. Once you get the hang of working with the changes, the archaic language itself isn’t inherently different in any insurmountable way, it just looks very different and stylistically it’s being used differently and for different purposes.