While you are right that this is indeed some of the "sacred music from this time period", there are some significant style differences.
The Hillsong song still is very pop chord-cyclic. Much of the song is dominated by a variation of a C minor - E flat major - B flat major - A flat style cycle -- essentially, I would call it vi I IV V (to my ears at first listen the song's "home base" is E flat at least). The chord pattern shifts a little bit from time to time and there is some occasional variation in chord choice -- for instance, later in the song the A flat gets substituted with a F minor (ii) -- and some chord order variation. But Hillsong (like a lot of modern pop music) more relies on texture and instrument density (or lack thereof) for their expression . (Here the repetitive nature itself also can be thought of as an element of expression I'm sure, repetitive chant is a well known element of various religious cultures.)
Bach's tunes were written in the counterpoint style, which is an entirely different way of composing (very much a voice leading dominated style, with a clearly defined function for various chords -- tonics, dominants, etc.). The Bach cantatas honestly are not comparable to Hillsong in some ways as I think they were more meant to be performed, not sung along with by the entire church. But the older unison singalong hymns also did not tend to lean on chord loops like modern pop.
Take Adolphe Adam's "O Holy Night" aka Cantique de Noel (link to a French choral-orchestral version found on Youtube -- https://www.youtube.com/watch?v=kNCFvg5M-yA). It "loops", but like most older hymns the loop is more verse-chorus oriented. You can have simple tunes with this structure ("Silent Night" is just three chords), but "O Holy Night" IMHO has a fair bit more complex chord progressions while still retaining enough simplicity to be a sing-along. Just to give one example, instead of repeating the chords at the end of the first part of the verse (I-V-I), the second part ends with a iii-VII7-iii so it can transition to the next section (in the Youtube version which appears to be in Eb major, that would be G minor - D7 major - G minor). The chorus goes through another set of chords entirely.
Personally, too often I find the Hillsong style of composing (which actually is very typical of modern secular pop as well) too repetitive for my personal taste, and lean more toward the older style. But this obviously is just my opinion. Hillsong is obviously popular, as is the modern pop style that they are written in.