I don’t use considerably more items hitting 14* vs 11* (I hit 11* earlier this year, while I was on a break). Outside of my strong titan colours, it can be difficult to hit the titan hard.
In the past, I would use big battle items regularly on 14*. I now let my teammates* help take care of those titans (instead of trying to force bigger hits with big items), and I push myself on my strong titans.
In other words, I try to play to my strengths: I allow myself to be (somewhat) carried on my weak titans, and I aim for big scores on my strong titans.
I can do more damage on a strong titan with bigger battle items, instead using same items for a small improvement on a weak titan.
*I’d say this can be alliance dependent. My alliance kills 14 stars non-stop.