At least to some extent they can be interchangeable. As for latha math vs deagh latha – you can use math in a general greeting, to say that the day is not particularly bad and deagh to emphasise that it is indeed good, at least according to this paper by Veronika Csonka:
We can also come across examples for starting a conversation: Latha math ann an-diugh, Uilleam., literally ‘Today’s a good day, William.’ which is halfway between a statement and the actual greeting. With regard to deagh-, it may function as an emphasising device: e.g. Thàinig an latha, agus deagh latha cuideachd... ‘The day came, and it was a good day indeed...’
And you can probably find more in her PhD thesis, eg. there is a listing of factors deciding whether to use a prefixing or a regular adjective:
This combined methodology revealed various factors that influence the choice between marked adjective + noun and unmarked noun + adjective constructions, including: (a) dialect (with the overall use of preceding adjectives in South Uist, but the preference for math ʻgood’ in Lewis); (b) register (ma(i)th in religious texts); (c) conceptualisation in the vocabulary (by the preceding adjectives deagh- ʻgood’ and droch- ʻbad’ qualifying abstract concepts, whereas the plain adjectives math ʻgood’ and dona ʻbad’ tangible and countable nouns); (d) pragmatic factors such as the emphatic nature of deagh- as opposed to math; and (e) grammatical factors (see the use of deagh-/droch- in subjunctive clauses, particularly in time expressions).
(Not a native speaker and I wrote the comment based just on skimming through those papers, so take it with a grain of salt)