Neither flag offends me, for it is a representation of something that has done no harm to me. On the other hand, I do find homosexuality to be both disgusting and sinful, but that is just religious bias.
I disagree with @Ninchaokin. A flag is a representation of the values behind it, it is a symbol, therefore the symbol of certain values can be offensive. I am offended by the flag of ISIS. I am not offended by the Confederate flag. I am certainly not offended by the gay flag. The one flag that you should not be offended by is the United States flag. If you are, pack your bags and leave immediately.
One of these has never been used at lynchings. One of these flags has never been used by recalcitrant slave-owners. One of these flags stands with people attempting to gain equality, the other with people denying equality. No, they both aren't offensive, only one.
@TBR The flag itself shouldn't offend you, I don't think. It should depend on how it's used. It's one thing to have it flown at a Civil War re-enactment or memorial, but it's another thing to have it hoisted at a KKK rally. It just depends on the situation.
I am offended by the Confederate flag but not because of the reason 9.9999% of people are. I am offended by it because of what it actually means. The components of the Confederate flag were all meant to be Christian, and when put into a sentence it basically means "This is a Christian nation and anyone who denies that is a horrible person".