In my rogue trader game there is a moon hidden inside a light-bending gravity anomaly that in the ages past during the dark age of technology was R&D station for the expanding human empire. An eldar transport ship crash landed on the moon after rupturing the webway and sealing the moon away from the outside world. The inevitable confrontation happened and after a war that nearly wiped both groups, their descendants signed a trouce.

They tried to create a mighty carrier, a mini craftworld if you like, strong enough to take them through the anomaly surrounding their relatively hostile home, but with the militaristic bent that both cultures have taken during their continuous engagment - many of their greatest wraithsmiths and engineers were already dead or at the end of their life. Repairing the eldar transport was unthinkable since the lack of steady source of solar energy meant that it would never be able to take flight.

Despite lacking much of the neccessary infrastructure, they salvaged the remains of the crashed ship and created a new one, using almost all of the available resources in the process. They worked so relentlessly, that at first they though that the efects of the fatal flaw in the ships fusion core was a mare sign of exhaustion and failed to reaile the truth until it was too late. With the ship all but finished, the remaining of their greatest minds died inside it from the leaking radioactive miasma and some even faced fate worse than death.

Striped from most of their resources and under the constant threat from the motated monstrocities pouring from their former hope of survival - their society detiorated into feudal state and sciency and technology became myths and magic.

In current days, my players have crashlanded on the planet as well, after making an uncalculated warp jump following the near fatal injury of their navigator during a loosing battle with a Battle Barge of the Emperor's children traitor legion. The natives, now a human/eldar hybrid with long lives, but very low fertility rate see them as the messiah from their legends (an amalgamation of the reborn Y'nnead and the Emperor), who will lead them to salvation. Their only hope to leave the planet is to cleanse the nearly finished ship from its mutant infestation, replace the tainted fusion core with their still inact plasma drive and brave the dangers of the gravity anomaly.

I want their (hopefully) newfound ship to look like the Bangal carrier from Star Citizen:
http://vignette3.wikia.nocookie.net/starcitizen/images/2/2f/Carrier_small.jpg/revision/latest?cb=20121117142536
https://s-media-cache-ak0.pinimg.com/736x/90/0a/b0/900ab01f815674463227ecaa18dcc627.jpg

I want the ship to be relatively small for the imperial standards (3 km long), but still able to almost stand up against an imperial cruiser in a fight.

What I am having trouble with is comming up with suitable statistics for the vesel. I want the ship to showcase both the achievements of the imperial and eldar technology. For armaments I'm thinking that two pulse lances (port and starboard) and an aft Jovian Patter Launch Bay (is there some better Launch Bays on Imperial origin that I am missing?) should be enough, since it is more of an exploration vessel and less of a gunboat, but I want it to have some other tricks in its sleave that my players will discover as the time goes. Does anyone have suggestions (have in mind that solar sails are out since the make little sence)?

Edited to remove unnecessary snark.

Your idea of the Solar Sails being useless is flawed. Given your back story, they aren't exactly useful for getting off the planet, but once out in the greater galaxy, they become useful once again for drawing power from stars, so I'd figure they'd still be there in some limited capacity, mostly as an augment to the human plasma drive, if not the primary power source. Also, you want your little hybrid ship to pack a heavy punch for its size, and by combining solar sails with a plasma drive, you suddenly get a vast amount of power to play with, because in essence, you now have two power generators. This will allow you to equip your vessel with the most power intensive weapons and components available, and far more of them than a ship its class could ever handle normally. You might not be able to power everything before the ship leaves, but you'll certainly have enough power once it does.

You said you want your ship to stand up to a cruiser, but you only have two guns, each limited in range of motion (port and starboard), meaning you only have one gun to bring to bear against a vessel at a time, and can't shoot anything directly in front of the ship. Eldar tend to go for dorsal and prow guns, and I figure a hybrid ship would be the same. This will allow you to bring both guns to bear on the same vessel most of the time, making your ship far more formidable in a one-on-one combat.

If you didn't know, there are stats for various Eldar/Dark Eldar ship components in several books. The CR, Hostile Acquisitions, and Lure of the Expanse all have fully statted Eldar components.

Given that the ship also uses DAoT human components, stocking it up with archaeotech human components would also beef up how formidable it is for its size. Indeed, I'd suggest using Archaeotech exclusively when picking out your human components. You said this was a DAoT research station, so it wouldn't make sense to use Imperial standard.

For particular components, I'd suggest having a Runecaster aboard the ship in place of a Navigator tower, incorporated into the bridge, to showcase the unique Eldar tech to the players in a place where they spend a lot of time. As far as archaeotech, I'd add the archaeotech bridge, and archaeotech lances. If you change your mind and keep the sails, an Energistic Conversation Matrix can turn much of this excess power into raw speed, surprising opponents (and your players) when the vessel suddenly accelerates to speeds incapable of escaping from or chasing down.

Really though, unless you base the hull off of an existing ship and solely use statted components, a vessel of this nature is going to mostly be a mess of homebrew, so make it however you want really. You seem to have an idea in your head, so I'd just go with that, and then work from there.