I'm not a cyclist, I do however do a fair bit of sailing where carbon fibre is often touted as 'the' material', so make what you will of the following.
Carbon is lighter than alloys or metals generally strength for strength, so a carbon component should be lighter than its metal equivalent. Carbon components can be made in a more engineered form (ie more material where required, complex curved shapes can be easier and cheaper than machined metal components.
all of which should lead to a lighter overall bike.
however that comes at a cost, often Carbon is horrendously expensive compared to a metal alternative. appropriate use can make huge benefits.... on a sailing boat that benefit can be in the hundreds of Kilos. whether it makes enough of a difference to a bike, at the level you cycle at (or aspire to) is a different argument. is shaving a few hundred of grams worth that much to you. can you make advantage of that weight saving.
I think that like many (male) dominated sports there are a large amount of ill informed gadget comments (this exists, therefore it must better), this is lighter it must be better, this is newer it must be better, brand X is used by team Y, therefore they must better. Many sports people (especailly at amateur level go down the route of I'm not doing as well as I expected.. it must be my shoes, bike, sails, whatever... whereas often the problem is the person themselves
What matters is can you get a performance benefit from using a Carbon frame?
Are there other things that you could do with the cash (either not spend it, get another more significant benefit from spending the same money elsewhere. who knows it mayy be that a carbon frame will make more sense in a few years time.