It's kind of strange to me to see so many people saying that the imperium would win 100% absolutely no contest what-so-ever. I think the empire could win quite easily:
- the hyperdrive the empire uses is a far more stable technology then the warp travel thingy the imperium uses (no getting lost in the warp, getting eaten by space demons, comming out in a different place or at a different time than you planned) and much much faster. This gives the empire a huge tactical advantage, and enables them to use hit and run tactics to hit key positions in the imperium.
This, i think is a far bigger problem for the impreium than many people think. I'm no expert, but as far as i've read (not that much, to be honest), the imperium is by no means as cohesive as some people think or as it should be. At times entire worlds are simply lost. Comunication fails, and contact is not established again for hundreds of years (or more, at times). And this is not counting the times when foul play is involved. Fringe worlds fade in and out of the imperium all the time (i read about certain crusades/expeditions/etc that brought back worlds into the imperium that had been forgotten for centuries, or millenia).
It takes the imperium months, and sometimes up to a year to reach some of the more isolated worlds, and even the central ones don't fare any better. In short, warp travel is considerably slower than hyperdrive travel. And mobility is a BIG deal.
- a lot of people point out that storm troopers can't shoot for shit. As the joke goes, that is true against main protagonists.

But in general they are quite competent. They were able to forge an empire after all, and they were cloned after a VERY competent individual. Plus, there are a lot of them. They are clones after all, they are easy to get in high numbers.
As far as the imperial guard is concerned, their greatest strength is "strength of numbers" also. As far as i've read about them (from their codex and other sources), the main strategy of the guard is just to overpower the enemy numerically, to crush them under a pile of bodies. Casualties are often times huge. I also think i've read that the life expectancy for the average guardsman once battle starts is 15 minutes. Also, a very common joke among warhammer players is that they are armed with flashlights. Generally guardsmen are effective in large numbers and with heavy support.
- the imperium is very close minded about technology. Progress exists but it is very very slow. A lot of technology has been lost entirely. I remember there were quite a few weapons and vehicles and stuff that couldn't be produced any more and the techpriest or whatever they were simply tried their best to maintain the ones that still existed. If one of those was lost, it was lost for good, and this generally tends to be their most advanced technology. And now that i've mentioned them: tech priests. The imperium is full of stupid superstition. They treat new technology with great fear and combine the one they have religion (machine spirits and prayers and rituals to them and other crap).
- the golden throne and the astronomican. As far as i know, the astronomican, powered by the emperor (and the souls of a lot of psykers per day) is what keeps space travel possible for the imperium. If the emperor dies, or the astronomican is destroyed, then the imperiums forces can't use warp travel anymore, as they need the beacon that the astronomican provides. This is a HUUUUUGE vulnerability. True, Holy Terra is well defended, but with the mobility the empire possesses, if it finds out about this, a single massive, well coordonated strike can end the imperiums warp travel capability. You can imagine the rest.
Like i said, i'm no expert as far as any of those two universes is concerned, but i think a lot of people are not thinking enough stuff through.