Your first line of defense against liability arising from the rental insurance is property insurance.
Your next is the fact that a suit against arising from ownership can only be brought against the LLC, although this works only if you don't personally participate in the conduct that gives rise to the liability.
For example, if the LLC hires a gas line repairman and he screws it up and the renters suffocate and die as a result, you probably don't have personal liability (assuming no other negligent acts on your part). But, if you did the gas line work yourself and you screw it up, then you would have personal liability, notwithstanding the existence of the LLC.
The best way to avoid personal liability for LLC acts is to vest management of the rental property owned by the LLC entirely in a property management company that enters into a contract to manage the property with the LLC rather than you personally, so that you have no involvement with anything that could give rise to liability. (You could also put a waiver of liability for mere negligence into the lease, but that wouldn't remove contractual or intentional or grossly negligent tort liability exposure.)
In cases where liability in excess of insurance coverage is limited to the LLC, then having an LLC with fewer assets is preferable to having an LLC with more assets, so paying off debt on the house rather than the rental first could advance the cause of asset protection.
But, the allocation of equity between the rental unit owned by the LLC and your home wouldn't make much of a difference in terms of liability to creditors unrelated to the rental property (e.g. you personally guarantee a business debt that goes bad, or get in a car accident), unless the equity in the home is protected by a homestead exemption in your jurisdiction.
Creditors couldn't necessarily get to the rental unit itself, but they could impose a "charging order" on the LLC that owns it, forbidding it from making distributions to you that aren't paid to the creditor instead, which would make it impossible for you to access the equity and rental income you planned on using to support yourself in your retirement.
Also, if you took so much equity out of the rental property LLC that the LLC was left insolvent or unable to pay its reasonably foreseeable debts (i.e. undercapitalized), then LLC creditors would probably be able to either recover from you because the removal of equity constituted a "fraudulent transfer" or under a "piercing the corporate veil" theory.