Essentially what the title says. Do Ascended careers have equivalent ranks in other systems?

Technically, yes. Ascended Careers are really just Rank 9 Dark Heresy characters, Rank 9 encompassing 13 000 - 16 999 experience.

In reality, however, no. The various advancement systems scale terribly between eachother, and the relative power level between two systems, with characters at the same experience level, does not correlate.

No matter what the system says, for example, a starting Rogue Trader character (5000xp) is not equal or comparable to a Dark Heresy character at 5000xp. I don't care what the books say.

I concur. Unfortunately, the systems are too different in terms of various special rules and traits. They "have" to be, as they all aim to depict different styles of gameplay, focus, and character vulnerability.

One could just compare the XP values (and this is the official suggestion for cross-product play), and certainly it is quite possible to have a good game like that (DH and RT are still somewhat compatible), but I predict a considerable chance to run into problems somewhere.

Personally, I would rather suggest trying to craft a character of comparable nature to the concept you want to play using the rules of the campaign's main game, and (if necessary) discussing possible houserules to accomodate the specific background of your idea.

Theoretically, they are also comparable to a starting level (13,000 XP) Deathwatch or Daemon Hunter marine.

but again, treat with large pinch of salt, as even those two clearly aren't comparable to one another:

The Deathwatch Tactical Marine, for example, has (in addition to assorted other niff-naff):

- a Bolter with Hellfire Bolts

- Bolter Mastery

- a Combat Knife

whilst the Grey Knight Strike Knight (his closest equivalent) has:

- Storm Bolter with Psybolts

- Swift Attack

- a Nemesis Force Sword

- Psy Rating 2 and several minor powers (e.g. Precognitive Dodge), even assuming he can't trigger 'proper' powers solo.

Plus a Personal Teleporter that he can use (with a Reaction!) to turn him into Nightcrawler in Powered Armour.

As stated above, you can quite happily drop ascension characters into rogue trader, deathwatch kill-marines into Dark Heresy, etc, etc. But you need to think them through a bit as a 'straight port over' won't be quite balanced.