I follow quite a few conference / event hashtags and have noticed that people often use the Storify tool / website to capture them. This is fine if there aren't too many tweets - as far as I can tell you still have to move each tweet individually (I've written a post over at Free Pint's FUMSI on how to use Storify) but two problems arise when the conference generates a lot of tweets (1) there's the danger that in clicking and dragging so many you'll get them out of order* and (2) it's a bit hard work.
*You can double click to move a tweet to the top, and if you hold down the shift key before double clicking the tweet will snap to the bottom of the list.
For larger numbers of tweets I've found Chirpstory to be the more pragmatic choice. You can move a page worth of tweets (I think it's 20 tweets [edit: I counted, it's 50]) so rather than having to do something to each one of 100 tweets you want to collect you can do it five times to five pages of them.
As well as that you can click a button to reverse the order of the tweets meaning that you can read the earliest tweet first.
I think Chirpstory is best suited to occasions when you want to bunch a couple to a few hundred tweets together as a record of an event and Storify seems best suited to fewer tweets where you want to add further commentary. You can add commentary in Chirpstory too but I prefer the Storify interface for that.
Obviously it does come down to personal preference but just in case you weren't aware of Chirpstory...
No Chirpstory don't pay me, I just find it a really really useful tool (as I do Storify) and I'm always on the lookout for info about tweet wrangling tools - see also A list of tools for finding or capturing tweets (30 May 2011, updated 14 October 2011)