it depends on the situation really, Heimer would be pretty good in terms of defending points from being captured, you would have to get through all his turrets first and by then the other team knows your there.
Panth would be good for capturing since he can jump to a point out of nowhere and capture away, and if he has aegis up thats a second longer to capture (wondering about that, do you cease capturing if ur simply attacked or only if you actually take damage? What about evasion/block?)
Certain tanks like Ali would be good because they could sneak around to capture a point and if they get interrupted they aren't automatically annihilated by the other team, they'd at least be able to get away or hold their ground for other people to come in and help. And in team fights Ali would be good since he has a stun and a knockback (usefull for interrupting captures too).
DPS champs have just as much a chance as well, an ambush on an enemy player (if it's right that these team fights will be mostly 1 v 1) could be devastating if they aren't a counter and defending capture points would be fairly easy unless they got ganked.
Stealth champs still lose no ground, you could think of capturing points simply as rushing towers while no one's looking, and sneaking past an enemy team would be much easier (if everyone's frequently dieing in team fights not many peeps would bother buying oracles unless they knew they could get away) Akali with a team would be good for capturing, just run in and chuck a stealth field then start capturing while ur team normally attacks them then pull out the cc's and stuns once ur stealth wears off (does capturing negate stealth effects? If so this is probably redundant)
So really it's almost an easy playing field for all champs.
Overall it's a fairly even playing field for all types of champs.