I've live in Lanzarote for the past three years and a further 3 years prior to that in Gran Can.
Gran Can is definately cheaper than Lanzarote, both for property and cost of living.
The problem with Lanza is that anything which is imported has to go to GC first of all and then come here, thus paying two lots of Port fees.
Aparently they are upgrading port custom facilities in Fuerteventura which would mean the retail companies would just need to ferry the stuff over in lorries which is expected to bring prices down.
In GC we rented a large 2 bed apartment for €550 in El Tablero. In Puerto Del Carmen you'd be lucky to get anything decent for that price.
We were forced to find a place in Playa Honda. 2 bed, first floor, in a residential area, very small, for the same price. 10-15 mins from PDC.
We currently live in a bungalow in Matagorda for €750 (bills included), but we could have got similar in Maspalomas in GC for around €600.
Rents aside it is the cost of living here that really shocked us. Prices are SO much more expensive for essentials
Our shopping bill in GC hardly ever went above €100 a week in GC, but here it seems we are never short of €140 a week (on average).
There IS a Lidl opening within the next year or so, so perhaps that will put a dent in the Monopoly of Hyperdino and Eurospar (they are the two biggest supermarkets here).
On the plus side... Lanzarote is a much nicer place to live. Very clean and the people are very friendly. It seems so much more laid back and less stressful. A damn sight less clique. The local councils appear to help Ex-pats with free Spanish lessons and a willingness to try to help wherever they can. There is a nice Ex-pat community who do a lot of good charity work for the benefit of the island and we even have 6 cricket teams here!
The weather is, of course, much better than the mainland.
Saying that,, it is not too clever this winter! I have to wear a shirt and long trousers! Wasn't doing that last year!
Given a choice I would pick Lanzarote over Gran Canaria every time.
Hope this helps.