Your personal financial condition will effect your LLC as I'm sure most of your vendors/suppliers require personal guarantees. In that event, if you file bankruptcy, it's going to hinder your ability to maintain and open new credit - because a personal bankruptcy will show up on a credit check for the personal guarantee.
Also, if your company files a Ch. 7, it will have to shut down,and you'll have to start up a new one. However, if you work in the same circles over and over, this could hinder your operations.
My advice to all clients is that bankruptcy should be the last option because it totally changes your life and will effect you for a decade or longer! Thus, all other options should be exhausted before filing.
With regard to the personal filing, you should try to work out a payment plan with the creditors. Contrary to popular belief, most creditors are willing to work out payment plans interest deferred/interest free - they don't want to see you file bankruptcy either (it guarantees that they won't get paid much, if anything).
Also, if you believe you can get your LLC's debts under control, there is certainly no reason to file.
If things get worse, you could consider filing a Ch. 13, which is a reorgainzation of debt. You get to keep all of your possessions and property and your debts are paid back over 3-5 years interest free. Because you're paying your debts instead of discharging them as in a Ch. 7, creditors don't view a Ch. 13 filing as a terrible thing - like they do with a Ch. 7.