So far 8.4 Beta 4 has been working great. The performance has been good. I like the new Music app. I haven't noticed a change in battery life yet. I am running it on my iPhone 5s and upgraded OTA from Beta 3. The only issue I have had so far is when I used Siri to call my Mom. I had told Siri who my mother was in my contacts so in previous versions of iOS you can just say "Call Mom at Home" and Siri would dial my moms home phone number. When I tried it after upgrading to 8.4 Beta 4, Siri came back and said "Sorry I am unable to do that for some reason" or "Something is wrong". I tried a few times but kept getting that error. However, after I rebooted my iPhone it was working again.
This isn't an issue with this specific Beta, but I am frustrated that Airplay is still glitchy as it has been since 8.0 was released on September 17, 2014. When I am playing a song in the Music player and then select the Airplay icon and choose my Airplay Speaker, after a few seconds the Airplay speaker will be deselected and then it will select the iPhone again (as if something crashes and resets) and it also clears out the music selection I was playing in the Music player. The work around is to stop the music, then select the Airplay speaker then start the music. I reported this bug to Apple over 6 months ago and then closed the ticket saying that it was a known issue. Oh well. Hopefully it is fixed in iOS 9.