Is there any performance advantage in using bottles with crowns / caps vs. bottles with swing top lids? Are the swing tops more vulnerable to loss of pressure? Any links to quantitative analysis or experiments would be nice.
In my experience, both work equally well. Where swing tops fail is repeated reuse of the seal on the swing top. Those eventually need to be replaced. They get less pliable with each washing/sanitation cycle. Can't give a specific cycle # because its multivariable dependent. Crown caps are one use only and hence the seal isn't an issue.
Can't help you with quantitative analysis or experiments. This is entirely based upon first hand experience and the experience of brewing friends.
We all moved away from swing tops as the seals started failing. Caps and craft beer bottles were cheaper than maintaining a fleet of flip tops.
I have used swing tops for over 10 years. In that time I may have had, at the very most, 10 failures. As brewchez states, swing top seal integrity is paramount. Replacement seals are readily available, and "a dime a dozen" if you purchase in bulk (200 or so). I now replace my seals on a regular basis, and have eliminated the failures referred to above.
By using swing tops, I restrict my brewing footprint by not possessing a bottle capper. Bottling is much more expedient if you are organized. Fill - seal, fill - seal... At the end of the bottling session, I use a tea towel to ensure exterior bottle surfaces are dry, as I did, many years ago, encounter a mould issue (you live and learn).
The only down side of which I am aware is that I am unable to submit swing top bottles in competitions. Not interested in brewing competitions, so it doesn't worry me.
Sorry, but no technical evidence. Only years of experience with my 300 plus collection of 450ml-500ml swing top bottles. Oh, and they are extremely strong, so breakages are less frequent (according to my UBrew4U operator whose services I used for 4 years before he ceased operations).