My method is very similar to PDF urist master's.
It's a very simple titan trap. Easy to set up early and can catch as many titans (or FB's) as you have room for.
It is simply a long hallway from your fort parallel to a long hallway from outside. Connect the two hallways with smaller, perpendicular hallways, and place a drawbridge at each end. Then place 1 or more doors inside the connecting hallway closest to the outside, remembering that building destroyers destroy buildings from 1 tile away (so 1 empty tile between the destroyer and the object). Link both bridges to a single lever, and you're good to go. In the above image, I use constructed walls to further limit which hall the titan goes to. Add a drawbridge (not shown in image) to the outside exit of the hall so you can seal the trap completely to do maintenance, reset some halls, or deal with a web titan.
If you catch a web titan:
Using the spacing between each hall to dig a down-stair to a silk farm is probably the simplest way to make use of your new asset. You may also use a similar setup for webbed traps, and dispense with using the individual halls (plus an idle dwarf) for catching your undesirable uncatchables. Be sure to completely block fort/outside access before releasing the webber. Understand, I have not vetted out the silk farm design shown here; last time I was able to do this was before DF2014 came out, and a simple cat-on-a-string would work. I took a look at the new wiki page for silk farms, and it seems you need a military dwarf to play bait and patrol in front of the web-slinger. So take my silk farm with a grain of salt. But this design will allow you to isolate a web titan in a silk/web-cage farm of your own design.
And if you want to remove the dwarf part out of the entire Titan/FB catching experience? My comment has an automatic design.
**Edit**
As for trapping web-slinging titans or FB's (immune to webs), the only thing I can think of is a cave-in cage trap. It works by using the dust thrown about during a cave in to knock the creature unconscious, which will cause them to be caught by a trap. No idea if it would work with a webbing FB or Titan, though I would think it would. So, 7x7 room full of cage traps, single block suspended by a Support in corner, web titan wanders in from one corner, destroys support in opposite corner, causes cave-in, gets knocked out on top of cage trap.