<logic:equal name="category" property="id" value='<bean:write name='idea' property='catid'/>/>
@here in side #2@
</logic:equal>
For option 2, you are not closing the value attribute of the logic:equal tag, you need a ' to enclose the bean:write tag, though this may just change the error, not fix it.
For option 1, I'm not sure you can nest a bean:write inside a logic tag (could someone confirm this?). You could try something like
I also think your logic may be flawed, you seem to be asking if the catid of the idea bean is equal to itself. This will alway be true, and hence there is no point in doing the evaluation in the first place as you can just do a bean:write.
Hope this is of help...