Alright there's been a lot of debate about the damage numbers between the two classes, but no real math yet, so I decided to do some. I did something similar in another thread comparing Operative damage with small arms full attacks against sniper rifles and small arms full attacks against small arm trick attacks.
I've compared Soldier and Solarion damage at 1st, 5th, 10th, and 20th level against ACs 10-50. At each level increment I've compared a Solarion full attack against a Soldier full attack. The numbers I used for everything are on the first page and the green bars on the charts are where the expected AC of equal level enemies are. Also while it's not in the sheet, full attacking is always better than doing a single attack at all levels with either class. The results are that at 1st and 5th level the Soldier does more damage, but the Solarian does more at 10th, 15th and 20th level. That said the differences aren't all that big.
Comparison Sheet
Things to consider:
Solarion
-Has lower AC and SP due to needing to divert points from Dex and Con into Cha. They also need to take the Heavy Armor Proficiency feat to keep up their AC. Some Revelations are lackluster.
+Has better social skill bonuses. Has a lot of in-combat tricks to do other than full attacking also gains some out-of-combat utility.
Soldier
-Can't do much in combat other than attack. Has no out-of-combat utility. Feats don't make up for class features. Some fighting styles are lackluster.
+Has higher AC and SP since they don't need Cha. Gains a bunch of feats which can be used to shore up defenses(iron will, lightning reflexes, etc) and later may make feat trees/combos easier to get.
Let me know what you guys think and if I made any errors.