At this point, I must admit that I wish I had a few of these older bottles today in storage - well, 2 -3 of each actually

The first rums that I really enjoyed were from Trinidad and Barbados, with Guyana and Jamaica following soon after. The problem in those days was availability - it was not easy to find things like Mount Gay XO, El Dorado 15yo etc. In Trinidad, where I lived for a while, what was readily available was the local brands, and these (Royal Oak, VAT19, Ferdi's) were also excellent in quality. All have since changed in flavour profile quite a bit.
In the last 7 years, my purchases of rum have been far more targeted, meaning I am looking for specifics. I have for the most part given up on "commercial" (big brand) rums, because they can be pretty much anything (even country of origin is often unclear!), and typically are sweetened to a point which sickens my-non-aspartame-nutrasweet-self. I do also find that as they bring new flagship rums out for a brand, they also simultaneously lower the quality of the old flagship rum. This has happened with Mount Gay, Appleton, El Dorado - heck, all of them almost.
As is, my money has been spent mostly on "indy-rums" - independently bottled, small-batch rums that can be clearly identified, with no additives, no added sugars, etc. My palate, which also likes bourbon, Scotch and Irish whiskies, definitely prefers dryer flavours - I don't have much of a sweet tooth, and also I've often noticed that all the added sweetness makes the product loose much of it's original character. So I've ended up purchasing bottlings from Berry Bros, Bristol Spirits, Velier, Gargano, Duncan Taylor, Cadenhead's, Silvano Samaroli's and so forth.
Sometimes people wonder, are rums collectable - and a big part of this is financial: Will the value of older bottlings actually start to increase dramatically in years to come, or not. I do not have the answer to this, but I have noted that recently the prices of some Italian indy-bottlings from Velier/Gargano have started to rise quite rapidly in the few webshops where they are still available at. For example, a few old Caronis from Gargano that were originally selling for less than 200 euros are now mostly not availabe - and where they are available, the asking price is over 400 euros. The big brand bottlings do not seem to fare nearly as well, which is interesting to note (in whiskies, original bottlings from the owner company do much better in terms of financial value than independent bottlings - but then again, in whisky no owner adds funny bits to their whiskies..).
I think this trend will be interesting to follow. Italy was the forerunner in whisky collecting, will we see a repeat in rums? A bit of a revolution going on there anyways, it seems.