I think it's just the military-esque drumming. The only difference is it works in this song, whereas it just felt weird on an Eminem album.
I think it's more the staccato delivery than it is the drums. Em's vocals are harsher where Mike's are smooth...I think it was Entertainment Weekly that called him "Eminem on Ambien"...but the rhythm of the delivery is very similar. Also somewhat similar to Kenji, but not as much. If Shinoda is spitting rhymes like Eminem minus the controversy, then the select songs with his raps will be phenomenal.
"Like Toy Soldiers" is in a minor key while "Hands Held High" is in a major key, so "Hands Held High" sounds slightly more optimistic. Also, there are no organs/strings in "Like Toy Soldiers", just the piano and bass. And of course, there are differences in the chorus, Eminem doesn't break into song at the end, and they tackle different subjects.