Such a comparison can be interesting but inevitable rather pointless. They are really at opposite ends of the filmusic spectrum; poles apart in so many ways.

DT wrote (usually) exhuberant, extrovert scores; loud, brash, thematically strong, and frequently calling attention to the music apart from the films themselves. (Example: his second Oscar winner, THE HIGH AND THE MIGHTY. Lovely, melodic and downright attention seeking from take-off thru much of the ride).

BH wrote (usually) highly effective, totally integrated scores which worked along WITH the picture. They seldom called attention to themselves unecessarily and usually saved mediocre films from utter disaster. (Example: THE GHOST AND MRS.MUIR, a quite dull and strange fantasy tale made into an exquisite love story merely with the addition of Bennie's gorgeous score).

The only thing is that many of Herrmann's scores only fully work in the context of the films themselves and thereby make for quite dreary disc listening (excluding the above example); many of Tiomkin's conversely are full of lively orchestrally powerful writing which can be used as effective "muzak" - as well as keeping the neighbours awake!