I don’t know if I would lump “all” protestants and “all” Catholics into one big generalization on this particular subject… But at the very least I can offer my personal experience from each side of the Tiber.
I think, as an evangelical protestant, I was more prone to memorize scriptures… (which is a GOOD thing!) but at the same time… there are many things I could not completely understand, or rather my understanding was based on the tenant of sola scriptura. For example, I would memorize passages that were dear to me, and apply my own understandings, or the understandings of my pastor/ Bible study leader to them… And often times, admitedly, I would just accept that I couldn’t completely understand what they were saying and just memorize them because the words were dear to me.
As a Catholic, I would say I’ve grown by God’s grace, in understanding the Scriptures as a whole, rather than passage by passage. In understanding the Church teachings about various subjects and Catholic theology, I find that when I open my Bible I see the continuity of Scripture much more clearly. Ideas and understandings I would never have come to “on my own” as a protestant, stand out in each page… Passages that once seemed unclear or to only have either a vague meaning, or a single application, now seem to have vast applications and “click” more than before. I see things flowing together more than before… And because I trust the Church’s understanding when I have questions or things that don’t make sense to me, I feel less likely to “go off track” when I try to apply and understand what I am reading.
I would say that now, I’m less prone to memorizing scripture, and more prone to soaking in the words more slowly, more delicately. Where I once read entire books and came away with a handful of messages, I now meditate on single chapters and see the Holy Words of Scripture as so much more than before.
Lastly, I would add that as I’ve grown in understanding of Catholic teaching, I’ve been able to understand many more concepts and messages of Scripture than before. I think a Catholic who knows his or her catechism for example, knows a great deal of what the Bible teaches. They are less likely, perhaps, to give “chapter and verse” but the Church teachings support Scripture so strongly that I think the average Catholic grasps more of the Bible than a “Bible alone” Christian would expect.
This is of course, my personal experience, but a personal change I have noticed since my husband and I swam the Tiber four years ago
my fault