Depends on how you interpret the setting.
If you actually look at what SW weapons can do, and to what extent SW shields can withstand those weapons, you come to the conclusion that SW is ludicrously over-powered compared to most other settings. It's been calculated that a single X-wing would be able to take on the Enterprise, for instance, and destroy it with ease.
I'm not an expert on 40K, but I think it's canonical that their bolters are more powerful than their lasguns. Or, approaching that the other way around: their energy weapons are weaker than high-grade kinetic weapons. But those kinetic weapons are a joke when faced with SW energy shields, just as anything 40K's Imperium has defensively is a joke compared to the SW energy weapons. That is: SW capital ships can easily Base Delta Zero any of the Imperium's planets, while the Imperium's weaponry won't even be able to penetrate the shielding of those SW ships. Meanwhile, the Imperium's methods of Exterminatus don't stand a chance of penetrating the planetary defences that even a lot of minor worlds in the SW setting possess.
The disparity is simply staggering. This isn't touching on the fact that the Warp doesn't exist in SW, so they can only move at sublight, whereas the hyperspace-capable SW ships can cross the galaxy in mere weeks (if not days).
Now, if you ignore the fridge logic of what SW weapons can demonstrably do (and how powerful they -- and, by comparison, all shielding -- must really be), and instead assume that the weapons of both settings are roughly of equal power... and that the Astartes magically get hyperdrive for all their ships... then I think an organised legion of super-soldiers, which is already extremely experienced, will over-run the complacent Galactic Republic within a very short span of time.