It's the same with the Unbidden. I was shocked when they started throwing several 100k fleets at me and I just had one ~120k fleet. So I attacked them when they came near my core worlds and expected a tough fight with me as a close winner but high casulties. In the end my kinetic artillery shot the crap out of them and I just lost 4-6 cruisers.
Seems like it really depends on your fleet-setup.
It does indeed.
I had the exact opposite experience to you with the Unbidden. I had gobbled up several Fallen Empires and had amassed an effectively invincible doomstack - 200+ endgame tech Battleships with Lances, Kinetic Artillery and multiple repeatable techs boosting them. This doomstack literally melted everything placed in front of it - even other doomstacks were generally destroyed before they got into a proper firing position - with ships being destroyed one by one as they entered firing range. It got to the point where I actually split my fleet on several occasions in order to avoid things becoming too easy.
I went into the battle with the Unbidden a lazy and overconfident Admiral. I believed I had every reason to be - my fleet had taken all comers during the earlier War in Heaven, and I outnumbered these Unbidden chaps over 3 to 1. Their main advantage seemed to be their strong shields - but I reassured myself that my ships' weapons worked best against shielded targets.
My glorious battleline opened up on the Unbidden menace with everything it had...
Only to find that my massed fire was utterly ineffective against them. Despite ravaging everyone else - the Unbidden were different - their ships dodged and weaved and evaded my fire - I could barely score a single hit on them. 200 Battleships worth of Tachyon Lances and Kinetic Artillery proved almost completely incapable of tracking their ghostly ships, managing a hit rate of barely more than 3%. Literally hundreds of thousands of damage points sailed harmlessly into the interstellar void - whilst the super accurate Unbidden disintegrator beams bypassed most of my shields and armor.
In the end - my short range point defence guns (Flak Cannons with decent tracking) ended up my most effective weapon during the battle - scoring more damage than my huge Kinetic Artillery guns. Dozens of battleships were lost whilst closing to point blank range to hit them with these flak peashooters.
It was a fantastic battle, a phyrric victory barely won at great cost, and I fully deserved the losses as punishment for my laziness in fleet design and shameful overconfidence.