Cheaper, probably. You won't know unless you shop around.
I do know that if you have insurance, your optometrist can't charge you any more for the eye exam than Pearle Vision will with the same insurance. But I would wager that you will get a more comprehensive exam from the optometrist in private practice than you will from the Pearle or Lenscrafters doctor.
My optometrist (a relative) worked at a chain when he first graduated from school. Patients were scheduled so close together that he couldn't do a dialation of the pupils to get a proper look at the retina. He hated the quality of care that he was providing but did it to pay the bills until he could go into private practice. They're your eyes. Make sure that you get the best possible care for them for your money. You won't get another pair.
As for the cost of the glasses or contacts. You might find that the optometrist is just as competitive as the chain stores. But if he isn't, don't be shy about asking for your prescription and taking it elsewhere. The price of the frames and lenses should also include free adjustments and minor repairs. For contact lenses, you should get a free trial pair to see if you're comfortable with them and your vision is clear. The contact lens manufacturers provide them to the optometrist for just that purpose, much like the pharmaceutical companies provide medical doctors with sample drugs for their patients. It can take more than a couple of fittings with contacts to make sure that you've got the right correction. My current prescription took 3 tries to get it right b/c they're bifocal contacts. Most optometrists in private practice will go that extra mile to keep a patient happy. Not all eyecare chains will.
As a consumer, I think that you're wise to shop around. Just make sure that your comparing apples to apples when you price-shop.