I like the motive bleeder because it fills your reservoir on the fly - pushes new fluid in while you are extracting it out through the caliper. I've never used the Griots suction type but it seems to me that you'd have to keep refilling the reservoir. With the Motive I just put the fluid in it, pump it up, and start bleeding without worrying about the fluid level getting too low
I have used both systems but the Griots I have does require a compressor, so it may not be the same one you are referring to. I prefer the Motive. Like Bob says, you don't have to worry about sucking air into the system. Plus I found the Griots suction system induces air bubbles into the line, so it is impossible to tell if you are getting air out of your brake lines or if is just the suction causing bubbles.
I own a Motive and have used the suction style nd the Motive is by far easier to use when bleeding all the brakes. The only advantage the suction style have is less setup and cleanup since your using the fluid in the MC reservoir, so for a quick bleed of one brake it would probably be faster and easier, For all other tasks, bleeding all 4 calipers, flushing the system, bleeding clutch hydraulics, the Motive is by far easier and more effective the the suction style. As a track junkie I don't know how I could do without the Motive.
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Go with the pressure system, Motive or Snap-On (Blue Point). Fast, easy and reliable if you keep the reservoir full. I used the suction system once in a pinch and the pedal never really firmed up, never could figure where they air came from. Later I used a pressure system and voila' problem solved.
I've also heard that the pressure bleeder is better for cars with ABS brakes, although I don't know all the technical rationale for that statement. In any event, the Motive bleeder has always done a great job for me on both ABS and non-ABS cars, and it is a lot less money than the Griot's device.
While the Griot's unit got a great write up as "tool of the month" in the latest European Car magazine I don't see how the price difference is justified. And as mentioned above, the pressure system avoids the chance of bleeding the master cylinder dry.
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