I have included requirements for both types of bonds in my RFPs and specifications over the years, mostly for government jobs, but also occasionally for some larger private jobs.
Collusion amongst contractors has historically been a problem in certain construction trades, with bids being manipulated so that certain contractors win certain jobs at a desired price point. Various contractors submit bids, and after bid opening, bids are withdrawn until the "appointed" contractor is the low bidder and wins the job. Bid bonds are one tool used to discourage this type of activity. These bonds also tend to prevent contractors from submitting frivolous bids just to "test the waters" without being seriously interested in winning the project.
Performance bonds, as you indicate, are designed to assure that a project gets completed as agreed upon. They typically cost between 1% and 3% of the total contract price. The companies who issue performance bonds are usually quite strict about who they issue bonds to, requiring the contractor to be financially stable as well as to have previous experience with jobs of a similar type and size. Because of this, requiring a performance bond tends to prequalify bidders, increasing the chances that only qualified companies will submit bids.
A joke in the industry states that if a contractor can obtain a bond, you probably won't need one, and if he can't, you probably will. In my experience, this is not too far from the truth.
Many smaller contractors and those just starting out have trouble qualifying for performance bonds, requiring that they partner with larger companies in order to bid on jobs. Some very large jobs (airports, seaports, etc.) have such rigorous bonding requirements that they are off-limits to all but the very largest of contractors. This is the how some of the big national and multinational security integrators seem to survive, despite their track record of mediocre performance.
Having a performance bond can be a hassle for the consultant/architect/engineer because the bonding company requires monthly written updates on how the job is progressing and on how payments are being made relative to the progress of the job. If a job is going poorly, the bonding company wants to know about it as early as possible.