For practical reasons, I have never come across any bilingual text, in any language, online except where the text in one language is followed by the other, with problems in navigating between the two versions. It's easy enough with print books, such as the Loeb editions, to print the translation on the page facing the original, but you can't do that with screens, except with split screens, which are awkward to use anyway. The only practical way is to use two devices - any two of desktop, laptop, tablet and smart phone - and have the original on one and the translation on the other. This has the advantage that you don't need to get both from the same site; just Google them separately. You can then fairly easily look from one to the other.

Such texts are rare anyway as they depend on volunteers digitising band proofreading, as with Project Gutenberg, so it's not really a question of favourites as there is often no choice.

However, if you're looking for bible versions, the Bible Gateway is a good one. I've used it for Septuagint, Vulgate and Ulfilas. Have one version on one device and your preferred English version on the other and you're sorted. There is the usual problem with translations, of course, but that would happen anyway.