As a one time 6 month trip, I think you are right on the boarder.
While the rental companies likely will give you a discount, renting
for 6 months is still going to be very expensive and likely they will have limits on where you can go with the boat.
If you buy: I assume you will want to buy a turn key boat prior to arriving as a couple months outfitting and repairing would eat up too much of your 6 months. That means a healthy chunk of cash up front as you won't want to mess around with boats that are "deals". Then having to pay someone to sell it after you leave while still paying for the care and maintenance
while waiting for a buyer. Plus you are on the hook for all the maintenance
until it sells. That's also not going to be cheap
and there is a big risk if you buy a lemon you may eat almost the entire price
of the boat.
If you had said 3 months, I would say rent as the cost of buying
would be relatively unchanged but the rental cost would likely drop by almost 50%.
If you had said 1 yr, renting
would be double over a 6 month lease
and you could include a couple months at the start to check out boats in person and do a little outfitting likely bringing down the purchase price
and reducing the chance of buying a lemon. Also you have the option to put the boat up for sale
a month or so before your are done to jump start the sales process.