The Imperium of Man knows how to use massed batteries of ultra heavy artillery. It's air wings are nothing to sneeze at either, especially in atmosphere. The Imperium has dedicated fighters, heavy bombers, strike aircraft, reconnaissance, you name it. LAAT Gunships are going to be target practice for battle hardened Imperial aces.
I feel as though I haven't made myself clear.
Yes, the Imperium has all these things. And I would argue that they make heavy use of all of them. It's not that they don't exist or are rarely used. Rather it's a matter of modernization of those concepts. You could for example, use modern technology today to wage a WWI or WWII style war, assuming both sides were intent to do so. And this is sort of what 40k and SW to an extent, do.
What I am arguing though, is that Star Wars has a style that is more in line with WWII and later day combat doctrines than the Imperium. This is impart because while Star Wars takes heavy inspiration from the two world wars, as does the Imperium, it also takes some more modernized inspirations of battles and tactical situations. In this case, a X-Wing is more akin to a Cold War style fighter, even though it still uses gunships that are closer to WWII American bombers.
Nor is that an argument that the Imperium or the Republic don't at all make use of more modern weaponries. Clone Wars gave us one of the more technologically sophisticated planets using megaton-level weapons to threaten anyone who attacked the capital city. And of course, the Imperium has their own versions of ICBMs--and they have no doubt used them more often than your casual mainstream sci-fi series.
But these are sort of far in the field. The majority of the franchises focuses more on epic-style invasions and wars.
Having said that, I am not sure the more forward facing methods of the Republic (and the Empire is actually regressive in a lot of its attitudes) is enough to offset the incredibly durable Space Marine forces. The two honestly fight in such a similar fashion that it's very difficult to say which one might actually think outside the box more. Although the Republic, under the command of the more liberal-minded Jedi (in the Locke sense, mind you), would probably be very quick to adopt a more modern style combat, because it would be their only choice against the more durable Space Marines.
Of course, the Space Marines also have their own version of liberals who might adopt a more forward looking combat style to suit them. And I must admit I am thinking more of 40k than say, 30k.
The Imperial Armada also engages at a far greater range than anything in Star Wars. Whilst they too like a good broadside, they'll do it from far beyond the naked eye.
Well, that's a little questionable.
It all comes down to certain realities of space combat that neither creative franchises really had any means of predicting, as space combat is still (at best) highly theoretical and limited to space combat simulators, which require certain levels of assumptions about future science and engineering capabilities.
What we have seen however, is that while ships can engage at very long distances with missiles and you could in theory do so with a very fast projectile, there are certain hard limits to this. For instance, anything that can hurl a solid mass at serious fractions of the speed of light is going to result in said slug shifting into plasma. It won't be so much that you hit the target with a sold mass, as it is that it's actually a flying explosion in space.
Now, setting aside massive rail guns or mass drivers, that brings back to the sci-fi staple of lasers and particle weapons. In this case, these weapons are going to be very limited to...I think a few dozen kilometers? And that would be the best case scenario for laser weapons. Particle weapons are even worse. To make matters even more complicated, both lasers and particle weapons can be affected by atmosphere and you may find that one which works well in space is complete shit in atmosphere.
Basically, in terms of combat range:
Missiles >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>solid projectiles >>>>> Lasers >>>> Particle Weapons
You can easily make an argument for two ships with the distance of earth between them launching drones or missiles at an enemy, but for projectiles, you're going to be generally limited to how quickly the projectile can reach the target vs how quickly the target can move. With energy weapons, you're going to be very limited in terms of range to dozens of kilometers in terms of doing real damage--although I think you can boost that range if you target low-armored targets and just let loose.
So in the context of a "realistic" engagement with how these weapons should act, what you would first see is the Imperium fleet is firing its prow-missiles at the Republic fleet. The Republic fleet, generally lacking any real sort of missile capability of their own, will launch their fighters. The Imperium will likewise follow.
The fighter fleets will struggle for superiority. The primary goal will be to either make way for the other's bombers fleet to reach the enemy or for one fighter force to defeat the other and therefore act as an early strike force for their fleet or as support in a more close-range battle.
In any case, whoever wins, what you'll see is the two sides closing to the range at which solid projectiles and really powerful energy weapons (more or less useless, but good for minor damage) will begin to fire. This I put fully in the hands of the Imperium, who generally have really powerful lances and lots and lots of macrocannons. If the Imperium's fighter fleet prevailed over the Republic's, you can expect that the Republican fleet will be wholly on the defensive. In fact, I'd say they'd be in rater dire straits. If the reverse is true, then what you might see is Republic fighters and bombers making attack runs on the Imperium fleet, even as the Republic takes heavy shelling. In which case, it might be more or less even.
Then you get into the area where energy weapons take over. At this point, Imperium energy weapons are probably powerful enough to bisect any heavily damaged ship or one whose shields have been compromised. On the other, you'll have a shitload of Republic laser fire raining down upon the Imperium. If the Imperium's fighter fleet prevailed, then the Republic was probably already crippled and is now in the process of complete and utter defeat. If not, then what you might have is a slugging match between the two sides. You can expect smaller Republic ships, if they aren't already out of the action, to be swiftly put out of action. However, any sort of ion cannon could prove devastating to the Imperium battleships, which are admittedly, somewhat backwards in their designs and may not be able to handle a weapon that causes that sort of secondary damage...of course, Imperium ships are also very redundant...
At best, I'd grant a Republic fleet maybe a 50/50 chance if their fighter/bomber fleet survived the confrontation with its Imperium counterpart. If it hadn't, then I would argue that the Republic fleet would probably be forced to withdraw or make a micro hyperspace jump to close the gap. Because as soon as they're trying to fight bombers AND missiles AND macrocannons, while not being able to return any sort of damage, the game is probably done.
I think for this sort of war, it would really come down to better strategic moves. I would argue that Imperium has a really strong pound for pound advantage...while massively outweighing the Republic to begin with, but I think it would actually come down to how the Republic deploys itself. It has the industrial, economic, and communicative advantage here. An Imperium fleet with 80 ships might be a match for 800 Republic ships, but the Republic will be able to coordinate and move faster than the Imperium can.
And before we assume they can just slap on a hyperdrive...that would probably require that they completely remodel an ancient ship whose worth is more than just its military value, but its historical and religious value as well. Imperium ships often take decades to construct and they are works of beauty, faith, and history. You're not going to get a quick new class of ships on any timescale that would be helpful for an immediate invasion.
So what you might have is the Imperium winning the battles, but losing the war. In which case, you'll have a sort of Tau situation; so long as it is within reasonable range of Horus's fleet that they can communicate and coordinate effectively, then the Republic probably won't be able to oust them, but step outside that and the Republic will outmaneuver and overwhelm the Space Marines.
That said, Horus might always rely upon the horrific incompetency of the Republic Senate. They are after all, horrifically corrupt, inept, and willfully blind to the problems around them. So much so that it was almost child's play for Palpatine to both become its leader, spawn the outer rim against the inner rim, and set himself up to become emperor...only to collapse within decades of forming.
Especially if the Confederate states were to join with the Imperium as distinct vassal states. Although the whole android army might make that...well, difficult.