An interesting topic that has been discussed several times before. The fact is that BW and JM serve rather different markets. BW is much older of course but is mostly dominant in the Eastern Caribbean. It has a near-monopoly in the Trinidad market (for better or worse) and has cornered the VFR market of the Eastern Caribbean. It has not been as successful with the tourist market though because the islands depend heavily on the UK and Europe for visitors and with its limited fleet it has not been able to offer the frequency and lower fares available with BA, VS and the holiday charter airlines. Nonetheless BW is still the de facto West Indian airline and its daily POS-BGI-ANU/SXM-KIN is the only regular daily link between Eastern and Western Caribbean capitals.
JM likewise serves the VFR market in Jamaica - although BW does come into its own there with the Caricom link. JM has been much more successful with the tourist market due to its aggressive marketing and tie-in with the Sandals and Beaches chains of hotels. Additionally, with Jamaica being more heavily dependent on US tourists (a market without major holiday carriers) JM has come to fill the role to some extent. JM's newer fleet has also been a strength for it. The large Jamaican community in the US has also helped JM, who can thus depend on the VFR during the off-season or if tourist numbers fall (eg post 11/9/2001). BW does not have that luxury in Europe beyond LHR.
JM has been more aggressive in expanding than BW, who has tended to stick to the familiar - but in the process JM has run up major losses and had some unsuccessful ventures like POS and EC Xpress. BW has also only recently curtailed losses but its financial base is still shaky, especially with the ICAO downgrade. To survive, though, BW needs to expand somewhat especially as the VFR market is not a growth market - especially considering how small the West Indian diaspora really is.
Overall, though, both airlines belong to the Caribbean and I hope that they both survive and thrive. I am Trini too and fly BW all the time but I would still give JM credit where it is due.
Hop to it, fly for life!