I just finished experimenting with invasion tactics! let me set up the situation.
I'm approaching the end of a very successful sandbox game playing Drath at crippling with version 2.02 TA. A mega event allows the Jagged Edge to take 47 planets including 34 of my planets. I can easily win a tech victory or with some patience, an ascension victory. Since the JE is a minor race I suppose I could go ahead and finish off the Yor and Korath Clan. Since those options don't go away, I decided to try to recover my lost planets.
First let me say that the advice offered by LTjim is great. I couldn't use info warfare since the JE planets were all 100% happy. I didn't have mini soldiers despite being very near the end of all branches in my tech tree.
Early in my recovery effort, I arrived with 10 transports loaded with 1.5B troops each, next to a pop 8B JE planet . Since this was soon after the JE coupe, the advantage and tech in battle were virtually identical. Lot's of reloads coming up. First I tried attacking with 15.0B, 10.5B and 6.0B 4 times each with Traditional Warfare. I won every time and the number of casualties I took was exclusively dependent on the invasion roll. With identical invasion rolls I took identical casualties with different size invasion forces.
Next I tried attacking with one transport at a time until I won. The resulting casualties were very close to the average of attacking with larger forces.
Next I tried attacking with a single transport of 1.5B using each of the invasion tactics I had available . Mass Driver was the most variable, sometimes taking out all 8B defenders and sometimes only a bit over half. The effectiveness and variability of Core Detonation, Tidal Disruption and Gas Warfare were most to least in that order.
Considering the very limited sample won't give very accurate projections and the fact that you will probably never have such closely matched advantages and tech in battle, here are some approximations. (JE Loss:My Loss)
Traditional Warfare 2:1, Mass Drivers 5:1, Core Detonation 4;1, Tidal Disruption 7;2 and Gas Warfare 3:1.
In conclusion, there is no advantage to attacking with overwhelming numbers. Attack with single transports using the most powerful tactic that won't conquer the planet until you can take it out with a single transport using traditional warfare. Smaller numbers of troops per transport give more flexibility.