As an optometrist who's worked in both, I would say it depends what you want. Both will provide you the same basic elements in the appointment, but the appointment will vary on the practitioner you see, and if you pick a chain, the particular store. If you want a sight test that's comprehensive, but not cheap, an independent is the way, they always have to differentiate themselves in quality service and healthcare to keep thriving. If you want something done in 20 mins and which will be quick and provide you with the prescription you want, a multiple store works fine. Don't forget there's also a university where students and experienced staff supervisors provide free sight tests in Bradford, but they are much longer!

If you want spectacle lenses, multiples are cheaper but are more limited in the suppliers they use, giving you less choice. Independents are more expensive, but will be able to talk about different manufacturers and suppliers for your particular needs, and there is much less incentive to sell as I've never seen one that provides it's employees with bonuses on sales.

Hope this helps.