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there is a big astrotrac thread in the landscape section you should read. You can compare the two. It comes down to how large of a rig you can accept and how long of a focal length you wish to use. The main downside to the Polarie is the polar scope goes where you attach the camera - you can't confirm precise polar alignment once you point your camera (there is the small port hole on the side for rough alignment), and payload limit is around 6 pounds.
If you have to travel light and do wide field astro landscapes - Polarie will make you happy. If you can pack a bit heavier, want super sharp tracking on a 200-500 mm lens (heavy) - Astrotrac. The Polarie has too much periodic error for the longer focal lengths - stars not as sharp and round.
There is also the Ioptron star/sky tracker which includes a polar scope for the price, but I have not read any comparative reviews vs the Polarie.
I have the polarie and love it. With wide field photography and not too long of an exposure, you should not even need the additional polarie polar scope. Your 135 would probably benefit from the polar scope so you can have 2-5 minute exposures. The Polarie polar scope is well made and extremely accurate for even 600mm fov exposures which are fun to do at times.
I confess, I have the astrotrac now too. I do enjoy using my 400mm lens as an option if I want to image some large astro objects, particularly if there is no appealing landscape before me. It's a matter of preferences. I kluged my polarie scope onto the astrotrac and it is amazing.
Your lenses - It is not unusual to need to stop down the aperture a bit to improve coma
the 35 1.4 has pretty bad coma wide open on full frame, and still some even on crop sensors. stop it down to 2.8 and it should be acceptable to you.
the 14 2.8 II has ok coma - bad on FF wide open but ok on crop. If you stop it down to f4, the coma will show very little on your full frame sensor.
the 135mm has no coma wide open.
So needing a longer exposure with your stopped down lenses will not be an issue with the Polarie! You'll have less noise, less coma and more detail.
Consider Manfrotto geared ball head in order to polar align your Polarie. Ballheads for alignment are very frustrating if not impossible to do accurately except for very wide and relatively short exposures. I am sure someone can do it without ripping their hair out.
You need cable release that allows you to program in your exposures.
Download and play with deep sky stacker once you are comfortable with single exposures and want multiple subs.
You'll need a downsizing stud adapter to screw into your ball head base in order to attach it to the smaller polarie screw stud. I forget the size but the polarie attachment stud is smaller than the standard tripod.
Sturdy tripod is a must.
Your 5DIII is an excellent camera body of course - live view focusing is a breeze, and low noise is wonderful.
In the end, it is the wide astro landscape that I find the most pleasing. The Polarie can do this well.