Eugh, nasty draw here for David Bowie.
The sound David Bowie has turned out for a long long time, starting with Spacy Oddity, and constantly changed his sound from glam rock, rock to soul. Hits like 'The Man Who Sold The World', 'Heroes', 'Life on Mars' make him a credible vote.
There's no denying the influence Rush have had on the rock music scene...Metallica, Smashing Pumpkinss and Dream Theatre among the bands counting them as musical influences, making them an easy choice on this on influence.
That being said, Bowie was one of the pioneers of glam rock, influencing bands of this genre, as well as a minor influence on a band known as Nirvana, with a reasonably famous cover of 'Man who Sold the World'. Personally, I'm giving Bowie the vote on preference, but I fully expect to be the minority on this one.