When it comes to technicality, based off of the recordings i've heard of Opeth and Dream Theater, JP is better, but as many (or all) of you have said that's not what counts.
As far as emotion i think they are both close. Sure the last couple of albums haven't been great (imo), but i find a lot of emotion from Images & Words to Scenes From A Memory, particularly in Awake and Falling Into Infinity. But you have to remember that emotion is subjective. Just because you don't feel emotion it doesn't mean others won't. And there are songs from each abnd that i find more emotional than other songs from each band. I feel more emotion when listening to Hell's Kitchen, Scarred, and Home than i do when listening to Hope Leaves, To Bid You Farewell, and White Cluster. On the other hand i feel more emotion when listening to In Mist She Was Standing, A Fair Judgement, and Blackwater Park than i do when listening to The Spirit Carries On, The Silent Man, and Take The Time.
The thing about comparing these two is that they are completely different. They are aiming for completely different styles. As somebody already said, Mikael takes care of music from a whole band perspective whereas with Dream Theater Petrucci wouldn't have that, at least nowhere near as much as Mike.
I think it depends on what mood i'm in and whatever i feel like listening to when it comes to who is better. That's all it rests on for me.