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Firstly, one of the rules of the forum is to not paste your log into your message. Use pastebin or the FTB log exporting features.
Secondly, you're using Java 7 which is why you're crashing. Mods have been making the switch off of Java 7 for the last 6 or so months and many packs will now...
It's difficult to diagnose your problem without a crashlog so I can see what's going on. My first question is, are you dedicating more than 4gb of RAM to the modpack?
Not according to the log you don't.
Memory: 619478928 bytes (590 MB) / 2775056384 bytes (2646 MB) up to 2863661056 bytes (2731 MB)
JVM Flags: 3 total; -Xmx3072m -Xms256m -XX:PermSize=256m
Minecraft has only 3gb dedicated to it.
This modifier is going to be removed in the next update. Any tools with the modifier currently will still keep the modifier. The fix to expand the blocks you can smash is to add the "blasting" modifier to the tool.