If you mean by stability if it works ok, both versions should work without problems.
If you mean bug-free (independent from the operating system), BG1:EE is pretty buggy. I have finished BG1 5 times, once classic, 3 times as BGT and once as BG:EE. First 4 (and many other half plays) were all smooth without encountering any bugs. However, EE experience took around 120 hours because of the game breaking bugs. Like quests not being able to finish, items disappearing from your inventory, map notes going crazy, Journal showing weird error messages when a quest is completed, some bosses (including the final boss) becoming non-hostile and non-attackable hence you can not proceed. Those are the ones I remember from my own experience. That's the final version btw so those bugs were never fixed.
You'll meet some people claiming the final version is bug-free. Those people either do not know what bug means or have not played the original so they think that's how things should be. Also, Beamdog, the company behind EE games which I supported many years, did something very "ugly". They deleted the bug reports provided by people including me. There were over 1 thousand (1000) bugs in the final version of BG1 2 years ago. Now that number is a lot less and my entries are deleted. If that's not an IT mistake, then they are deleting bugs to show the game does not have any bugs which are definitely not the case.
On the other hand, EEs do have some nice touches to them. I liked the new Character and Inventory interfaces although many hated it. Being able to dual-wield while having a bow in extra weapon slot is very handy. So is the "see everything on the ground" button. However, do not expect any "graphical enhancements". EE game characters, buildings etc, is exactly the same as the original at best and a lot lot lot lot lot worse than the original at worst. "Enhanced" only stands for the interface, zoom function etc.
BTW: My experience is mostly on BG1. I never finished BG2 although I started it million times :)
Great answer, thanks. It made my decision harder, but now I have good grounds to ponder on.
Bascially it seems to boil down to extra material and quality of life changes at the cost of more bugs. I've seen reviews mentioning problems witch crasches too, so the Enhanced Editions seems kinda unstable in spite of being 5 years old.