I think that might be the reverse that Ratner was more agreeable with 20th Century Fox. If memory serves, the budget was set before Ratner came on board during pre-production after Vaughn bailed. It's very likely, unlike Singer, he was fine with what he was given and didn't push for more. I can see this given the surface-deep nature of his other films.
The budget actually
ballooned when Ratner came on-board. I believe the budget was around $175-$200 million when Matthew Vaughn was slated to direct but after Ratner came on-board the budget apparently skyrocketed to over $225 million. At least that's what
Empire reported.
According to Box Office Mojo, the purported production budget was $210 million. Comparatively speaking, the budget for
X-Men was $75 million and the budget for
X2 was $110 million. Ratner essentially had another $100 million more to work with than Singer had on
X2.
Singer wanted the Danger Room, he wanted Sentinels, and he wanted bigger action sequences (as well as more breathing room for other characters like Angel). 20th Century Fox repeatedly denied him those things. Brett Ratner wanted the Danger Room, he wanted Sentinels (they weren't in the script before he came on-board; he reveals this in the commentary) and he wanted big action sequences and he got them. In my view, there's some faulty logic there. It seems 20th Century Fox should have been more flexible with Singer and had that happened he wouldn't have been enticed to jump ship. They were perfectly willing to accommodate Ratner and his needs but not Singer's.