John Wells's polls among native speakers showed:
AmE: θ - 84%, đ - 16%;
BrE: đ - 85%, θ - 15% (though in Scotland this rises to 82%)
Wells, John(2008) Longman Pronunciation Dictionary (3rd edn), Harlow: PearsonLongman.

Other
I've got myself used to using "with" as wiθ but on tv or the internet I hear it mostly as wiđ. According to some dictionaries that I've consulted to, only the version with the voiceless th is correct. So I wonder if it is a BrE/AE thing or it changes from one person to other. I particularly welcome the answers of the members who are from different English-speaking countries, although it is not a must.
Thanks for your answers in advance.
John Wells's polls among native speakers showed:
AmE: θ - 84%, đ - 16%;
BrE: đ - 85%, θ - 15% (though in Scotland this rises to 82%)
Wells, John(2008) Longman Pronunciation Dictionary (3rd edn), Harlow: PearsonLongman.
That sort of information, very useful at times, is one of the reasons I recommend that book - 'Longman Pronouncing Dictionary' by J C Wells
Buy your own copy!............
He doesn't give poll figures, but gives /đ/ as the first, /θ/ as the second in withal, withdraw, withhold, within, without, withstand, and notwithstanding; He reverses the order for the second th in forthwith. He makes no mention of AmE for any of these.
Roach et al give both for with, noting 'The pronunciation with θ is most frequently found when followed by a voiceless consonant (e.g. 'with care)'.
They give: withal (đ), within, without (đ, BrE, đ,θ, AmE), withdraw, withhold (đ,θ), withstand (đ,θ, BrE; θ,đ, AmE), notwithstanding, forthwith (θ,đ)
Roach, Peter, Hartman, James & Setter, Jane (2003 edn*) Cambridge English Pronouncing Dictionary, Cambridge: CUP
*This edition is the 16th edition of Daniel Jones's English Pronouncing Dictionary, the second to be edited by Roach et al.
I don't think I ever heard wi[θ]out!![]()
/wɪθaʊt/ sample
without pronunciation: How to pronounce without in English