I have a two part question about planet defense:

First, what determines your chances of conquering a planet? I imagine it has something to do with your total attack + any invasion bonuses / the planets attack + defense.

and second, which of the two kind of structures better protect your planet from invasion, a structure that adds an invasion defense bonus like solder outpost...+300 invasion defense OR a structure that adds defense like mass shields...add 450 defense.

(and I am just talking about odds of conquering, NOT other dynamics that make a planet more difficult to take or will require the attacker to use more energy)

There's a thread somewhere around here that has the invasion chance formula.

As for which is better, it depends on the specific structures. 400 Defense is better than 400 Invasion Defense, just because they're equal for the invasion chance but defense also lowers the damage they do. However, standard defense structures can be destroyed with Saboteur or Crimson Cluster Missiles, so they aren't reliable on a planet that's good enough to use Crimson Cluster Missiles on. Also, Invasion Defense structures usually give more invasion defense per space than standard defense structures, depending on your tech level. Thus, it's difficult to say which is the best necessarily, it depends on the specific structures and the planet to be used on. A number of my planets have 4 of the +1200 attack/defense structures, but my Colossal Gaia only has two; however, this is because I use a number of special structures instead, because anybody who scans it might be willing to use 4 Crimson Cluster Missiles, so I must rely on other means of protection.

Your chances of conquering a planet is determined by your total attack, including buffs and invasion attack, in comparison to the planet's defense/attack/invasion defense totaled. There is an equation for it out there, but I don't know it. However, the higher your attack, the better your odds.

Invasion defense, attack, and planetary defense all contribute evenly to stopping an invasion attempt, so whatever structure/artifact give the highest numerical value per space is best.

OK, interesting, so there is no real difference btw structures that add invasion bonus and defenses, my research is pretty high for my level so I never used solder outpost and such, by the time I got the solder outpost I had planetary shields, but was curious if there was any difference they put in the math calculations, thanks for replying, now about to look up that formula.

Planetary defense is used to determine the amount of damage you do to the planet with each attack, invasion defense is planetary defense + any invasion defense structures, and is used to determine your invasion chance of the planet.
Here is the thread discussing planet invasion chance: viewtopic.php?f=4&t=7514