Really interesting topic!
I'm not sure how much of a military threat the Star Empire would be against the Federation post-Nemesis.
Even if they joined the Dominion War late, they suffered considerable losses (including their flagship). However, as others have pointed out, according to Sloan they would be in the best position to threaten the UFP.
But then Shinzon happened. While that upheaval might be overstated, that has to contribute to their diminished influence. If only in political terms. Now they have to deal with the Remans uprising. They have to deal with the political ramifications of being part of a plot to be aggressive against the UFP. Then again, throughout Trek the Romulans constantly engaged in plots to hurt the Federation (brainwashing Geordi to assassinate a Klingon or trying to steal the Prometheus
) yet the Federation just laughs it off and forgives them...
Then their sun going nova or being caught in that "wave" from the Hobus star. Yes. They're an interstellar empire and thus...can probably survive that. But the idea that the loss of Romulus and Remus (which was a source of dilithium) would not affect them in any major way is laughable... It would set them back. A lot.
There is no argument that out of the major powers, the Federation got out of all these vents with the best standing.
Having said that....
Barring the Romulan-Earth War and the Dominion War, the Romulans don't seem to usually engage in open military conflicts. They seem to rather use subterfuge, sabotage, manipulation, etc. CIA/KGB tactics to bring down governments. So even with all the set backs they've suffered, the Romulans could still engage in these tactics to "bring down" the Federation.