Telomeres do not "cause" ageing as such - although you are right that they limit the number of times a somatic cell can divide.
Each time a cell divides the chromosomes are replicated in an imperfect way, and as such a small amount of DNA is lost from the end of the chromosome during each round of cell division. Telomeres are just extensions to the chromosomes, so that the DNA that is lost is not important. When a cell runs out of telomeres it ceases to divide.
However it is a big generalization to say that telomere length is therefore correlated with lifespan. For instance a recent study has shown that mice have telomeres 5-10x the length of humans, but live 30x shorter (1).
Inter-species differences in lifespan
Whilst I am no expert on these 2 plants, it is quite an obvious thing to say that organisms age at different rates. Mice, for instance, live 3 years in a protective environment, whereas humans can live 30x that. The difference is down to the life strategies acquired by natural selection: it is more advantageous for a mouse to develop very fast to reproductive maturity and have as many offspring as possible, because there is a very high mortality rate for mice. Conversely for humans, in takes more than a decade for us to reach reproductive maturity! Our "rate" of development/ageing is lower, which is completely related to our reproductive strategies.
I imagine that a very similar story is true for plants - for some it will be advantageous for them to "live fast, die young", whereas for others the best strategy might be to take a long time creating less, but more robust, offspring.
At the molecular level
I have answered a related question previously (Do trees age on a microscopic level?) which might be of interest to you.
In short, the phenotype of ageing is associated with irreparable damage at the molecular level - be it to DNA, organelles, protein aggregations... you name it! Organisms that have a higher metabolic rate, such as mice, accumulate this damage faster. This gives them the benefit of being able to reproduce much earlier, at the cost of reduced overall lifespan.
Plants age slightly differently, but at the genetic level much the same repair pathways are conserved throughout the kingdoms of life, with some alterations of course - for instance plants seem almost completely immune to cancer (2)!
As I argue in the linked to question above, plants have a potentially indefinite replicative potential, as every cell has the capability of regenerating its telomeres, because plants do not have a conserved germ line as animals do - any cutting from a plant has the potential to create an entirely new plant. This varies from plant to plant of course, and plants are still susceptible to damage, they just have modified/adapted repair pathways to cope with their specific lifestyle.
You ask whether it is the telomeres or the "rate" that differs between the plants - the answer is almost certainly a combination of both, amongst the other myriad of factors that influence lifespan!
- Colado, et al, 2013. Telomere dynamics in mice and humans. Seminars in hematology [PubMed]
- Doonan & Sablowski, 2010. Walls around tumours - why plants do not develop cancer. Nature reviews cancer [DOI]