Actually, to my knowledge, the Doomsday Machine was said to be a highly advanced piece of technology coated in Neutronium alloy (which is impervious to conventional weapons ... therefore, SF as we know it in TNG, DS9 and VPY would essentially be in more or less same predicament as Kirk's era SF).
The problem I see with this though is that SF should be far more advanced than what it was shown to be in TNG.
Almost a century before TNG started, they essentially disabled a Doomsday Machine which sported some highly advanced technology.
One would expect of SF to be able to develop Neutronium based alloys (or alloys partly made out of them) by TNG era and have even more-so devastating weapons (not to mention shields and much faster Warp capability).
A problem that cropped up is that the writers who made the show didn't know how to deal with highly advanced tech as part of everyday life of SF and they ended up forgetting about it the next week (just look at how dumbed-down everything is on-screen when taking into consideration the technology which was presented).
Jono - you beat me to the Neutronium explanation ... and I would actually agree that SF as it was depicted in the 24th century, they would be able to simply drop a warp core into the mouth of the Doomsday Machine and then be on their way.