The battery bleed while in sleep mode appears worse than ICS on all three of my Android devices.
On my SGS3, the battery drains a lot more on ICS than JB when in airplane mode. For the most part, battery life is better on JB than on ICS when in sleep mode except one time a month ago where it seemed to drain unusually fast. When using the phone, battery life between the two have been the same. That is my experience.
People said Gingerbread was better than ICS. They said the same thing about the battery life. And the same thing was said about Froyo to Gingerbread. I liked all of them. The battery life might be better on ICS due to less features. I must say, I would not want to go back. I like Jellybean. Can't wait for 4.1.2 and 4.2.2. Also looking forward to Key Lime Pie.
GB had better battery life than Froyo on my HTC Desire Z. Performance was a bit better on Froyo than on GB. It seemed to be a trade-off between better battery life on GB and better performance on Froyo.
I have Nova but never use it. I will have to try Apex.
I use Nova and it works great on JB. There are 2 things that I do not like about JB. First is that when you do not set up a default app, like a browser, under ICS, you are presented a list and you just have to tap the app you want to use and it launches it. Under JB, you have to tap the app and then you have to also tap <Just Once> or <Always>. It's like JB wants to annoy me into selecting default apps. This pisses me off.
The other issue I have is with the default music widget on the GS3. I configure Nova Prime to have 6 rows of icons (and no app tray). Normally, you have 4 rows of icons with an app tray (or equivalent of 5 rows). Under ICS, my 4x1 music player widget looks fine. Under JB, my 4x1 music player widget cuts off the name of the song which is displayed on the bottom of the widget. The widget cuts off the bottom third of the text line that displays the song and artist name. If I make it 4x2, then I can see the name without it being cut off.
For everything else, I really like JB. I am very happy with the update. I actually held off upgrading for a while because I already liked my phone running ICS. Once it seemed like JB is pretty good, I did the upgrade. There will always be people with issues here and there with any phone running any OS version.