Stability has never been an issue for me of However I don't mount extra things off of my stands. I have the pre-atlas Ludwig flat base stand that are super light weight. I don not use a flat-base hi-hat stand or snare stands. Snare stands are lightweight and compact enough and I have not really had a chance to try out flat base hi-hat stands besides an old Ludwig Standard that I really like. I use these stands for a 16" K custom fast crash (lightweight), 20" K custom dry ride (Super Heavy) and a 18" Armand Beautiful Baby (medium weigh) they hold up well and also the Dry ride sounds better on it. I never thought that cymbal stands contributed to the sound of a cymbal but they do.
I have no problems positioning these stands.
As for cons; if you like to mount extra things off of your stands (toms, extra cymbals, etc.) It may not work as well but I have not tried it and my stands are much more lightweight than the newer Flat base stands.
Edit: Saying that the stands make the cymbals sound different is a very small thing not noticed unless you are right up on the cymbal, so I wouldn't call that a pro or con.