I would say Gran Canaria, I have been to Lanzarote, GC, La Palma and Tenerife in November all have had hot weather but last year in GC it was 30°+ Of course you can't guarantee good weather

If you're in the south of each island, the weather will be much the same, but Lanzarote fares slightly best being furthers east.

As I too am considering Gran Canaria or Lanzarote for a birthday holiday in November, I did a little research and compared the daily weather history of both for the 2nd half of November going back to 2000. Although the temperatures were very much the same, it was quite noticeable that Lanzarote had more 'mostly cloudy' periods during the day than Gran Canaria but less rain.

I used wunderground's weather history facility as they have always been pretty accurate whenever I have compared the weather I've had on holiday to what they say it was. I'm not sure where the weather station they use is in Lanzarote (maybe it's Costa Teguise which can be cloudier) but the Gran Canaria weather report was for Las Palmas which is in the north of the island.

Do they not use the airport readings for both islands ?

Looks like you are right Big Al. The weather station location for Gran Canaria is GCLP which is Las Palmas airport and the location for Lanzarote is GCRR which is Arrecife airport. Go to the top of the class.

Gran Canaria generally has a bit better and more stabile weather than the other islands.