Question: I am trying to pick a physics engine for a simple software application. It would be to simulate a rather small number of objects so performance isn't a huge concern. I am mostly concerned with the accuracy of the motion involved. I would also like the engine to be cross-platform between windows/linux/mac and usable with c++ code. I was looking at Bullet, Newton Game Dynamics, and ODE because they are open source. However, if Havok/PhysX are significantly more accurate I would consider those too.

All I seem to find are opinions on the engines, are there any thorough comparisons between the options? Or does anyone have experience trying the various engines out. Since what I'm trying to do is relatively simple there probably isn't a huge difference between them, but I'd like to hear what people have to say about the options? Thanks!

Answer: 
There is a nice comparison of ODE and Bullet here:

<http://blog.wolfire.com/2010/03/Comparing-ODE-and-Bullet>

Hope it can be useful in making a choice.
Sorry, but you will never find a real comparison with respect to accuracy. I am searching for three months now for my master thesis and have not found it. So I started to do the comparison on my own but it's still a long way to go. I'm testing with 3d engines and even 2d engines and for now Chipmunk is the one with the highest accuracy so far. So if you have no need for 3d I would reccomend it. However if you have an urgent need for 3d and your problem is as simple as you described it (don't want to expand it in the future?) Bullet and ODE will do it. I would prefer Bullet because it is much more up-to-date and is still actively maintained. At least there is Newton, with which I am fighting right now. Therefore I can't give you pros and cons except that it is a bit more work to get familiar with the (crucial) bad documentation.
Hope that helps. Best regards.