There is a book that came out a few years ago that seems fairly popular, called A Guide to the Good Life: The Ancient Art of Stoic Joy, (here) by William Irvine. He has succeeded in capturing the true spirit of the Greek and Roman philosophers who espoused this way of life. He notes that even Marcus Aurelius, the Roman Emperor who wrote about his Stoic views , ignored the Stoic teachings on logic and cosmology, and focused on the ethical core of the Stoic tradition.
This is also what Irvine does, looking at how Stoicism can be applied to our 21st century lives. He does this in an even-handed manner, trying to produce the best arguments against each Stoic principle and practice as he outlines them, and then attempting to come up with a valid response to these objections. Not every writer does this.
As far as Buddhism is concerned, by comparison, Irvine is honest in his personal reaction, that it is too different or oriental for him, and that its meditation practice too time consuming. I think both of these objections are wrong, but I won’t go into that here. He does note many similarities between Stoic and Buddhist teachings, especially regarding compassion and living a life of simplicity and integrity.
The one thing Buddhism has in its favor compared to Stoicism is the combined physical and mental practice of sitting meditation. Stoicism has various mental practices as recalling the events of the day before going to bed and evaluating them. This of course is not meditation but contemplation, of which the Buddhists also have many varieties. But I think one of the reasons why Buddhism survived in a continuous lineage for so long compared to the Stoic tradition dissipating in late Roman times, is its foundation on the integration of body and mind in the formal practice of sitting meditation.