That is, do you think a tempo of say 109.36 would be exactly the same in Logic, Pro Tools or Vegas?

There is no reason to think it wouldn't be. 

I think the characteristics of the file will probably produce more bariatric on than the DAW

I know one person who got varing results with ableton and pro tools and were so alarmed by it they reverted to 2" analogue tape. They claim the offset was perfect. Maybe an extreme reaction..

Having said that I had no issue importing a wav created in cakewalk into an entirely seperate mac pro tools project with same bpm without referencing each other (no auto stretching).

I'd be interested to hear people gotchas here it's an interesting topic..

That sounds like a sample rate mismatch Alex not a tempo problem. 

Overall I have found tempos to be accurate but sometimes over the course of a longish tune for example it may need to be adjusted slightly in one DAW compared to another.
 
What to do.
 
If you are thinking of migrating a session from one DAW to another a good thing to do is to somehow while the session is in the original DAW create a click audio track that represents the metronome. So let’s say you are in your starting DAW and the tempo is 100 BPM.
 
Create an audio track for the metronome. You can do it in Sonar even if you have to route things and do it all in real time. (Studio One can now render out the whole metronome track in one flash now. THIS is a great feature and I hope others do it as well)
 
Drag the session into your receiving DAW including the metronome audio track and start by setting the tempo there also to 100 BPM.  Move all the tracks around including the metronome audio (you may not have to anyway) until everything lines up with the grid at the start of the second DAW.
 
Now go right to the end of the session and see how things are holding up there. eg last 4 bars etc. Often it will be spot on but sometimes I have had to make a very slight adjustment to the new DAW tempo eg 99.97 or 100.02 etc in order for perfection at the end as well. Make sure your tracks don't timestretch when you do this too. (Sonar cannot timestretch tracks on the fly anyway so you should be good to go) The receiving DAW might though. If it does then the error will still be there at the end.
 
The metronome audio is more accurate than relying on the music to do this.
 

Computers have crystal-controlled clocks, IIRC typically within accuracy of 0.01%. They're not locked to an atomic clock...if you take different digital devices, set them to the exact same tempo, and tell them to run, they're going to drift.
 
My main experience with drift is with flying in audio from a handheld recorder with camcorder audio. Even with both being crystal-controlled and set to the same sample rate, after a couple minutes, you hear the drift. Round about three minutes, it becomes sufficient you have to do some fixes.
 
It would be interesting to run some tests, but I suppose the hard part would be finding something with sufficient timing accuracy to provide a standard of comparison.

+1 to that... I cannot resist myself when kicking the bees nest at engineering discussions by bringing up tolerances, and more importantly stack tolerances (how they combine). Understanding tolerances is "basic" engineering, yet so many seem to neglect this once they move to "higher levels." As soon as you begin calculations on things with "high accuracy" it quickly decays into three significant digits and an order of magnitude being the "real number." Calculations only carry forward significant digits of the least accurate component, and this gets neglected often, as does the precision of the device doing the measurement (the +/-).
 
It is incredibly easy to spin up engineers when they give you "numbers" and the first question asked of them is "What is the +/- for these?"
 
Being from places where Cs beam repeaters (atomic clocks set to the world standard) are required, debating variances that fall within tolerances is a bit moot.

Jeff Evans
 
What to do.
 
If you are thinking of migrating a session from one DAW to another a good thing to do is to somehow while the session is in the original DAW create a click audio track that represents the metronome. 

Thanks Jeff,
 This is a great idea.
 
 I have been using Cubase's auto Tempo Match feature because it works fantastically well. I have been exporting the audio scratch track and a MIDI reference file so I can use them in another DAW for multi track drum tracking and editing.
 The idea of including a audio click track in the export is a very helpful idea.

Computers' timekeeping is perfectly inaccurate.