I am voting for the Rakatan Empire for the situation that you described, when the Reapers arrival is noticed and an all out war is fought between the two. The advantages of replenishing ships/weaponry from the Star Forge and having hyperdrive to be able to harass their enemies would be enough to deal with the reapers fairly quickly.
However, using tactics more similar to their strategy in Mass Effect, I think the Reapers would be more likely to win. If they approached unnoticed and scouted/indoctrinated minor worlds, the Reapers could potentially learn about the Star Forge and attack it quickly. Without the Star Forge, the Rakatan Empire would be wiped out completely.
As for the spaceship tech differences the OP mentioned, I think the shields by both sides would be effective at slowing down the other sides fire. The shields used in Star Wars are used to block missile strikes in addition to lasers, and at least the humans/others in Mass Effect had some small degree of energy weaponry that the Reapers were deflecting. Because of this, I think they would be close to even in space engagements with the war being won by unlimited reinforcements from the Star Forge.
Ground battles would be won by the Reapers simply through bombardment from space or indoctrination. They would use species from the Star Wars galaxy, and in the games that we learn about Rakatans, rancors were pretty common so they could be made into larger versions of brutes. The force could potentially protect some of the rakatans from being indoctrinated themselves, but I do not think this would protect the majority of them anymore than the biotic abilities of the Asari. Also the slave races would be mostly vulnerable to indoctrination, providing the Reapers much large/better ground forces.
As a slightly related note, in the extended universe the star wars galaxy does get invaded from another galaxy that uses a strategy close to what I described for the Reapers without indoctrination.[footnote]http://http//starwars.wikia.com/wiki/Yuuzhan_Vong_Empire[/footnote] This other group was able to invade without being noticed until their arrival, which leads me to think the Rakatans would be more likely focusing on threats inside the galaxy rather than an outside invasion.
TLDR: Rakatans win the all out war described by the OP, Reapers win a slower invasion that learns of the Star Forge and deals with it quickly.