It is going to really depend on your state's property tax laws and the appreciation in value of your home.
If your state has a homestead exemption on property tax, then your llc is not going to qualify for homestead exemption. So your property tax bill will be higher.
You will not qualify for Section 121 Capital Gains Exclusion on your primary residence if your LLC owns the house. You will have to depreciate the house over 23.5 years, but this amount will be recaptured at 25% when you sell. You can do a 1031 exchange, but pay the extra fees, while it would have been tax free for nothing in your own name.
Your property insurance will most likely be higher as you have to pay for a landlord policy owned by the llc and a renters policy in your name.
The yearly fees and taxes on the llc will add up depending upon the state that you are located. The additional paperwork and forms will add up. Depending on where you live, the local jurisdiction may require your llc to have a business license and pay more taxes.
Unless your house is free and clear, it would violated Due on Sale clause. Yes not likely to be invoked now, but it is a possibility.
Asset protection this will be neutral unless the LLC has another member besides you.
I don't see how you would deduct utilities unless they were provided in the rent. The IRS will want to make sure this is a true market rent if they figure out you are renting to yourself.
In summary, I don't think the tax savings in deductions would outweigh what I have listed unless you think your market will not appreciate. If you think that, then you are better off just renting from someone else anyway.