Not necessarily.
mini-rant: Depends on how all-out. Hermann Kahn, the Cold-War Theorist who was one of three inspirations for the character of Dr. Strangelove, with such lovely book titles as
On Thermonuclear War,
Thinking about the Unthinkable, and
On Escalation, was a staple of my tween years. He theorized the existence of a "Escalation ladder". Whereas most thinking about Nuclear Weapons traditionally imagines that Nuclear weapons are a very simple "Yes/No" value, he argued that Nuclear Weapons had their place on the "ladder" of confrontation, where the bottom rung is "Ostensible Crisis" and the Top rung is "Spasm or Insensate Nuclear Warfare", and everything else inbetween covers everything else, from shows of force to legal and diplomatic sanctions, from limited conventional warfare, to Nuclear Ultimatums, and from Local "Exemplary" use of nuclear weapons to limited military usage, all the way up to targeting of civilians to various extents. No such crisis needed to go through every single step on the ladder, he thought, so a situation COULD just develop straight to "general nuking of everything", but it need not. There are stages between using war and nuclear war, and there are stages between local nuclear war or military nuclear war and the popular image of sending 50-megaton bombs to all the major cities. I'd say that this ladder would only become more diverse and complicated when different types of WMDs are used with wildly different capabilities, so the space version of the Escalation ladder must be pretty complex.
Arguably, that ladder is also one of the biggest issues with hypothetical wars in general. With a hypothetical war you have to "assume" that one stage or another is being used, when reality might be different. The Federation here might be superior in one localized, "conventional" space conflict limited to one solar system, while the Empire might clearly win out in any sort of multi-system war, while perhaps the Federation has a significant when it comes to a localized military-targeted WMD-using conflict, while perhaps the Empire has a slight advantage when it comes to "blindly flinging the strongest bombs we have at any target that presents itself." We might end by saying that the one who is best at the last stage wins, but the issue is that the results of a real war will depend on what stage is actually used, and when, whether, and how much the rung of escalation changes (can't nuke anyone if you lose your entire fleet in conventional warfare, for example). Do the Federation and the Empire start off by flinging both the regular and jury-rigged WMDs at major population centers? Most wars don't start that way. In fact, no war has ever started that way. And if they don't start that way, when do they get there? These are questions the Armchair general must answer.
TL;DR In short, I'd say it's impossible to analyze how a "real" war would go between the two, while it might be worthwhile to figure out who has the advantage in a variety of different scenarios, and then guess from there what that means.