The merits of rubber

[Odds]

I'm looking for a roof-guy to fix my leaky lead over a bay window and i keep getting told a rubber roof is a better option; is this true?
It looks like the kind of rubber i'd use on a bicycle inner tube, so what's the optimum thickness to keep out rain and snow?
They say it should last up to 50 years but the lead over my bay window has been there since the house was built in the 1930s, so why would a rubber option be best in the long run?

 

[datarebal]

Because they probably can not fit lead correctly, and know it..so opt for epdm

 

[Odds]

Yep, i had a feeling that's why they keep plugging rubber on me. Is there a particular type i should be aware of?

 

[datarebal]

Firestone is probably market leader