Dīpa is a homonym, which, as noted earlier, stands for two distinct Sanskrit words, “island” and “lamp”. So neither is “better”, it depends on the context. Given that the two words are completely distinct, however, it is safe to assume that, apart from poetic or otherwise unusual contexts, one or other meaning is correct.
In this case, dīpa in the sense of “island” is a standard term used in a series of quasi-synonyms at eg AN 3.51, AN 3.52, and SN 42.7:
tāṇañca leṇañca dīpañca saraṇañca parāyaṇañca
shelter, protection, island, refuge, and haven
All these have the sense of “safe place”. In the passage alluded to at the beginning, which occurs in the Mahaparinibbana (DN 16) and several other suttas, attadīpa is paralleled with attasaraṇa, and thus clearly has the sense of “island”.
attadīpā viharatha attasaraṇā anaññasaraṇā, dhammadīpā dhammasaraṇā anaññasaraṇā
Live with yourself as your own island and refuge, and no other refuge, with the teaching as your island and refuge, and no other refuge.
This is confirmed by Sanskrit parallels of this passage. In the Mahāvastu of the Mahāsaṅghika-Lokuttarvādins we have (Mvu31#14):
ātmadvīpā bhikṣavo viharatha ananyadvīpāḥ ātmaśaraṇāḥ ananyaśaraṇāḥ dharmadvīpā ananyadvīpāḥ dharmaśaraṇā ananyaśaraṇāḥ
And in another passage from the same text (Mvu95#9)
ātmadvīpā bhikṣavo viharatha ananyadvīpā ātmaśaraṇā ananyaśaraṇā dharmadvīpā dharmaśaraṇā ananyaśaraṇā
While in the (Mūla) Sarvāstivāda Mahāparinirvāṇa Sūtra we have:
ātmadvīpair vihartavyam ātmaśaraṇair dharmadvīpair dharmaśaraṇair ananyadvīpair ananyaśaraṇaiḥ
There’s no really difficult interpretive problem here. Reading this passage as “lamp” was an old mistake made by Thomas Rhys Davids in his Buddhist Suttas of 1881, uncritically echoed in spiritual pop culture ever since.
This mistake proved congenial to those who wished to prove that Buddhism was merely a restatement of the Upanishadic atman theories. Such theories were lent an unfortunate respectability by Caroline Rhys Davids in later years, but I don’t think her husband Thomas was of the same persuasion. You still find this kind of thing today. As just as random example, from Buddha and Shakespeare: Eastern Dharma, Western Drama by David Jon Peckinpaugh:
The Buddha: ‘be a lamp unto yourself,’ reminds us that we can all end up adding this very illumination to the symphony of Light that is the Cosmos in Radiant Manifestation, as the very Lila (Play) of the Divine Incarnate here and now … and now … and yet again, now.
(This quote is a master class in pseudo-spiritual bullshit. Note the use of capitals—even for the Sanskrit! Wow, it must Be So Very Important. The archaic “unto” gives it that Biblical touch. And it’s not just “illumination”, but “very” illumination, another archaism which, coincidentally or not, was favored by some early Buddhist translators. The Buddha is said to “remind us”: but does he, really? Or is the author just making stuff up that has no relation to the text, and using suggestion to try to convince uncritical readers that he has access to a profound universal wisdom?)
Anyway, ‘island’ was clearly used as a term meaning “refuge, safe haven”. The interesting problem is not whether it means “lamp”, but how to render the sense into English. For of course, the English idiom is that to make yourself an island means to cut yourself off from humanity, and not in a healthy way. The Pali sense is of dry land in a flood, as noted by @suravira (which, by the way, awesome name: “Hero of Heroes”! Or does it mean “Liquor Hero”? Without diacriticals, I can’t tell.)
This is, presumably, where the sense of “help, support” is derived from. I don’t think they quite hit the mark, but perhaps “haven” or “sanctuary” might do.
Live with yourself as your own haven and refuge, and no other refuge, with the teaching as your haven and refuge, and no other refuge.