Yes, independent contractors are liable for their acts and omissions
The contract between the contractor and the principal should set out what the contractor is expected to do and the standard to which they are expected to do it.
If the contract does not set this out then they will be required to perform to the standard of a reasonable person doing that sort of work plus any statutory requirements. So, if they are a plumber, then they are required to install the plumbing to the applicable building codes and to the standard that a reasonably competent plumber would do so.
If they fail to do the work or fail to do it to the required standard then they are liable for any damages the principal suffers as a result.
Further, an independent contractor is liable for any tort that they may commit against a third party. So, to continue the plumber example, if the plumber negligently installs pipe for a builder and that pipe breaks damaging a tenant's goods (i.e someone outside the contractual chain), then that tenant can sue the plumber for negligence but cannot sue the builder or landlord.
Employees are the same but also different
Employers are vicariously liable to third parties for the acts and omissions of their employees except where they are on a frolic of their own (i.e. doing something that is clearly outside the scope of their employment).
At common law, the employee is also liable to the third party and the employer, however, such claims are rarely pursued because a) where there is insurance, the employee is also covered b) the employee may lack the assets to meet the damages and so be "judgement proof" c) it's really bad PR and d) many jurisdictions prohibit it by statute (e.g. new-south-wales).
Protection for an independent contractor
Insurance
Public & product liability certainly. Motor vehicle insurance if applicable. Professional indemnity insurance if the work is of a "professional" nature, that is, involves providing advice rather than just goods and services.
Protection for an employee
Insurance
Check that your employer has the right insurance and that it covers their employees.
Is it better to be an employee or an IC of said company to avoid this type of liability?
Like you have a choice.
The nature of the relationship will determine if you are an IC or an employee. If you are clearly running an independent business then you are an independent contractor. If you are clearly a wage or salary earner then you are an employee. If it's unclear, you are still one or the other and you don't get to choose. See Indepdendent/Contractor vs Regular Employee