Should I go for a reach str based investigator or a dex based with a level of inspired blade swashbuckler?
Str will have a bigger damage output, reach, power attack, and I don't have to multiclass, but I get a penalty to my int when I mutagen.
while the dex will make for higher AC and I'll get some parries.
Hmmm....this is an actual tough decision for investigators. I mean, alchemists, they have bad will saves, so dex means lowering that further.
But investigators....
Still, I love reach builds. Grab some lunge to go with that, since it lets you leave enemies outside of your threatened area. That means enemies have move 10' to reach you, and they draw an AoO and most likely lose their full attack. So it can actually be a better defense than just plain AC.
The fortuitous property is also a big incentive on top of that. With this +1 property, 1/round when you get an AoO, you can get a second one in there at BAB-5. That is basically a full attack in your AoO. So that can really punish anything that tries to get to you.
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Strength will give you more umph for your buck with a combat investigator as you will have to devote less feats and gold into getting what you would like. Plus as you have already mentioned, Power Attack will aide you quite a bit.
Whichever route you go, though, for a combat investigator you should select half-elf due to their FCB. Couple that with Combat Inspiration, Amazing Inspiration, and an Inspired weapon, you really start dishing out some decent damage. At 12th level you can spend 1 point of your Inspiration to add 1d8+3x2+5 damage to your attack. Which works out to 13-27 additional damage on top of all your other normal bonuses (this includes Studied Combat of course).
Reach/Strength is complimented by a lot of the extracts, even at low level (long arm & enlarge person) and strength works better with the powerful polymorph extracts at higher levels, since the better forms are larger and hence give strength bonuses.