Can I assume you saw these two options in St Vincent and The Grenadines? If you need to incorporate just for offshore banking purposes, the form of the company doesn't really matter. LLC is usually less expensive in terms of incorporation, but has more expensive annual fees than an IBC. For both you can always add the nominees to protect your privacy.
The difference is in the official company documents (IBC has Shares Certificate and Memorandum and Articles, LLC has Membership and Operating Agreement/By-Laws accordingly) and the officers (IBC has Shareholders and Directors, LLC has Members and Managers).
Regarding the suffixes: IBC can have Ltd, Limited, Inc, Corp etc, LLC can only have LLC.