I truly doubt DS9 had a higher budget than DW.
Adjusted for inflation, it probably did. Fifteen years ago, DS9
's budget was in the $1.4 million range per an episode. Even eight years ago, when the Eccleston season was airing, Battlestar Galactica
cost $1.6 million an episode. Doctor Who
's budget is in the £1.0 million range per episode.
On a similar note, I wouldn't be at all surprised if Elementary
spends more on one 45 minute episode than Sherlock
spends on one 90 minute episode.