The first crash I had was an block ID conflict (Seemed strange to crash rather than the normal generation of IDconflicts.txt)

But this one now that I've fixed the block IDs (moved blocks to 4040-4052) it seems to give this strange crash report which I can't translate at all.

java.lang.IndexOutOfBoundsException: Index: 0, Size: 0
at java.util.ArrayList.rangeCheck(Unknown Source)
at java.util.ArrayList.get(Unknown Source)
at erogenousbeef.bigreactors.common.BigReactors.register(BigReactors.java:251)
at erogenousbeef.bigreactors.common.BRLoader.load(BRLoader.java:86)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
at java.lang.reflect.Method.invoke(Unknown Source)
at cpw.mods.fml.common.FMLModContainer.handleModStateEvent(FMLModContainer.java:545)

Full crash log here: http://pastebin.com/1UPwZ1L0

I'm not using MineFactory Reloaded, but usually that'll result in an error when calling an external class if it tries to call something not there so I don't think it's a dependency issue.

I tried removing all sorts of mods to see what might be conflicting, till I got fed up and removed ALL of them except BigReactors and it was still breaking, so I deleted the config and voila, it runs!

Changing stuff doesn't seem to be breaking though.
Here's the config file that was breaking it, this is what was generated during the crash of the item conflict. I edited the block IDs to fix the conflict: http://pastebin.com/rSLDjvZ2
And here's a default generated when BigReactors is the only mod: http://pastebin.com/QU5S541A

EDIT: changing block IDs to 4040-4052 worked fine, and then so did adding back in all the mods. It just seemed to be a config file issue, but I have no idea what the issue is.

Ah, I see the issue. The problem is that you had the registerYelloriteSmeltToUranium flag set to true, registerYelloriumAsUranium set to false, and no other mods which provided an ingotUranium. BR then tried to look for the first type of ore registered as ingotUranium, found none, and barfed.

I'll fix this, thanks for the report.