I can give a partial answer, on the reasons for preferring the codex format and the timeline, but I'm afraid I can't give any info on relative durability.

Why prefer the codex? 'Codex' is the technical name for a book made by binding pages at a spine. The main reason for preferring it historically was that it allowed much bigger volumes than a scroll did, and the storage space required was consequently smaller. Our earliest reference in the textual tradition to commercial use of codices by ancient booksellers is in an epigram by the Roman poet Martial, writing in the 1st century CE. He reports that he is impressed after seeing a codex edition of Ovid's Metamorphoses with the entire text in one volume (Martial, Epigrams 14.192):

haec tibi multiplici quae structa est massa tabella,
    carmina Nasonis quinque decemque gerit.

Look at this bulk! It's built out of many­-layered leaves,
    and holds fifteen books of Naso's poem.

The Metamorphoses is about 78,000 words over 12,000 lines, so this is enormously beyond the scale of what a single scroll could practically achieve.

There is a catch: while a single codex can hold enormously more text than a single scroll reasonably can, (a) it isn't nearly as easy to keep on adding to it -- with a scroll you can just add more papyrus sheets at the end, with a codex you need to rebind the whole thing; (b) up until the modern era, storing multiple codices could actually take more storage space than storing a bunch of scrolls with the same amount of text, because codices were stored flat, not upright, and because they were too large to pile them up (see for example this illustration from the 8th century Codex Amiatinus).

The timeline. Lionel Casson's Libraries in the ancient world (2001), pp. 127-8, reports on how papyrus finds in Egypt are divided up between scroll and codex format in the following proportions, which change depending on date:

	Scroll	Codex
1st-2nd centuries CE	98.5%	1.5%
ca. 300 CE	50%	50%
ca. 400 CE	20%	80%
ca. 500 CE	10%	90%

So the codex caught on reasonably quickly in the Roman world after its commercial introduction in the late 1st century. There is one area where it caught on even faster: Christians preferred the codex almost immediately. We have a number of papyri of Christian texts, some from the 2nd century, and heaps and heaps from the 3rd century onwards, and it so happens that there are only one or two that come from scrolls. The imbalance in Christian texts is very striking in comparison with non-Christian texts. We don't have any documented reason why Christians preferred the codex format, so it's open to speculation (anti-Jewish sentiment, based on the fact that Jews strongly favoured scrolls? Who knows). But it seems plausible to me that the Christian preference for the codex boosted its adoption rate in the 3rd century.