Since the Liturgy of the Hours is prayed by all sorts of people everywhere in the world at given times of the day, it is an official, corporate prayer of the Church, even if recited privately. You’re still praying “in common.” On the other hand, the rosary is a private devotion. Lay people are encouraged to pray the Liturgy of the Hours, the ordained and many religious orders are required to pray it. So a lay person, praying at her breakfast table or on the living room sofa, is praying right along with all those other folks.
Personally, I like the Liturgy of the Hours, and pray that more consistently than the rosary, but then again, most days I pray the rosary as well.
Since I usually just pray from the book Christian Prayer, I usually just pray Morning Prayer, Evening Prayer, and Night Prayer. Morning Prayer gets prayed (I’m a middle aged working laywoman) when I get up, whether it’s 5 AM on a workday or 8 AM on a day off. Evening Prayer gets prayed anytime between quitting time and 9 PM. Night Prayer gets prayed before I go to bed. What I like about the Liturgy of the Hours is that the psalms, readings, and prayers are varied from day to day. I don’t have a full four volume set of the Liturgy of the Hours, I use the somewhat abbreviated Christian Prayer. Basically, each prayer period takes about ten minutes or so, hardly onerous. Even if you just decide to pick one Hour to pray, it still has the effect of setting the tone for your day (if you decide on the Morning Prayer,) or summing up your day (in the case of Evening Prayer.)
If you want something that is a little less varied, you could try the Little Office of the Blessed Virgin Mary (it’s shorter, but there are still prayers at specific times of the day.) It repeats the same every day.
But to answer your question (I hope,) if you do not belong to a religious order which requires praying the Liturgy of the Hours, there’s no requirement to do it at all. Nor is there a requirement to pray the rosary. If you’re a lay person, it’s strictly personal preference, so there is no criterion for making this decision. You can download an app and see if the LOTH resonates with you, or try the rosary to see if that works better for you.
And don’t be surprised, either, if as your life circumstances change, so do your prayer preferences.
In other words, it’s all good.