So I won the Captain Sim 777 in the contest they had about year ago, and I got the PMDG 777 the day it came out. I wanted to see what one was better and find the pros and the cons of each one. So let me start
Models:
Captain Sim has everything for the 777 out, the -300ER,-200LR,-200ER and the -200LRF. PMDG only has the -200LR and -200LRF out, with the -300ER on the way (knowing PMDG in a few months) So I had to do this test with the LR Model, and I had the same plane, same paint, at the same airport during the same conditions. I chose Air Canada 777-200LR, and flew out of Toronto Person Intl.
External looks:
Captain Sim 777 has a good exterior, I like the paint they did, shiny but not to shiny, unlike PMDG's where it is very shiny. Some parts are very well detailed, like you expect from Captain Sim. PMDG also has some very good detailed parts. One of the best on PMDG's is when you get on the breaks for an RTO, and the brakes turn red hot. Here are some comparison pictures.
Captain Sim Exterior:

PMDG Exterior:

Another big thing on the Triple 7 is the wing flex. CS has very minimal wingflex compared to PMDG:
Captain Sim Wingflex:

PMDG Wingflex:

The 777-200LR has the most powerful engines in the world on her, the GE90's which produce 115,000LBf of thrust. Both do a good job of modeling the engines from the first class cabin.
Captain Sim:

PMDG:

After landing, I got some pictures of the Speed Breaks and reversers when I touched down.
Captain Sim:

PMDG:

Sounds:
Watch a YouTube Video with the GE90's roaring, and you will want that in your 777 on FSX. I honestly think that PMDG did a better job with the sounds, by CS is also very good, and they got theirs from Turbine Sound Studio, well PMDG did it on there own. on the CS one, when your in a wing view, you hear the external sound of the engine, and it is the same sound no matter where you are viewing the plane from. PMDG on the other hand, is the internal sound, and everytime you change position, you get a different noise, like you would on a real aircraft. PMDG has a different sound for every single button, switch, and lever, well CS is using recycled sounds from past airplanes.
Cockpit:
Now were getting to the good stuff. CS's has an Electronic Flight Bag (EFB) tha hold your Approach, STAR, Departure, and SID and Airport charts. It is great to use, and it is very realistic. CS also has a working weather radar, and terrain. But, like in other CS models, it does lack some stuff which is important to the experience. Some of settings, like the checklist and other MFDS doesn't work, which is a bummer. PMDG on the other hand doesn't have an EFB, or weather radar. But everything else is like you would get in a real 777. the FMS and MFDS all have working settings, everything works, every system and every knob, switch and button does something. You also get to see the mechanical cover move when you press something in the PMDG model, it is just awesome! you get all the failures, and even ground opp setting in the PMDG's FMS. Here are some cockpit shots. Sorry for the blurriness, I have to figure out how to upload at the new settings.
CS Full Cockpit:

PMDG Full Cockpit:

CS Detail:

PMDG Detail:

I then wanted to see the difference of the PFD, MFDS and ECAS:
Captain Sim:

PMDG:

Conclusion:
Captain Sim Pros:
-Good value compared to PMDG
-Sounds are good
-External and VC are well detailed
-All models are available
-EFB and Weather Radar
Captain Sim Cons:
-Flight Systems are not like a real 777
-Autopilot is unrealistic
-Some systems do not work.
-Engine Start is unrealistic
-FPS Heavy
PMDG Pros:
-Flight Dynamics
-Sounds
-Detail
-Autopilot and FMS
-Night Lighting
and many more
PMDG Cons:
-PRICE
- Only the LR and LRF is available
I think the PMDG is the best, hand down, but this is my opinion, I'm a real work pilot and like realism.