Archaeology BA or BScWatch
However, no not really.
It really depends on the university & what you want to focus on. I did the BSc and there are more compulsory modules ie. Stats & “arch science” modules, but other than that and the requisite that you do a data driven dissertation eg. stats or lab based dissertation not really.
some unis for BSc ask for a “science” A-level and some unis entry requirements are higher for the BSc - Altho this differs at each university, so isn’t a set rule. Although, with any degree if you can’t decide look at what modules you have to take between the two degrees & compare them at different unis. As archaeology degrees, vary widely at unis. ie. Southampton - maritime. Exeter - experimental. reading - romans.
But, generally content doesn’t really differ and doing a BA still means you can do all the science modules you want (generally) Altho, comp / core modules may mean you have less freedom to chose (either way).
tdlr: no not really.