I was looking at some old figures and came across both Archangel and Falcon who both had the same titled and worded SP:
These came out right around when I stopped playing and I've never played them that I can remember, but I'm not sure if I'm interpreting this right or not... after the Charge, they would still have to breakaway to finish their half-movement, right? It's not worded like HSS where you make an attack during your move so I want to make sure I'm not assuming too much (between the wording at the time and minor updates to wording since then, too).

That is how it has been ruled so you would be correct.

For comparison, see Beast from the M&M set of Archangel.

Yeah, that's what I was afraid of. Thanks, guys.

This particular issue is one of my pet peeves...

There is this clarification in the Player's Guide:

When using Fly-By, if Falcon chooses to use the rest of his halved movement, and he starts the movement adjacent to a character from which he has not yet broken away this turn, he would need to roll break away normally.

While the ruling has been consistently what Harpua said, this text in the Player's Guide does not actually support the ruling. The offending word here is "normally". You do not normally have to roll for break away if you are not given an action to move and Falcon/Archangel are not given an action when they continue their movement, so doing this "normally" would mean not rolling for break away.

The simple fix here is of course to just remove the word "normally" from that clarification.

So wait... he could start adjacent to someone, breakaway, move away (let's say with the Suit of Sorrows so he can grab an object), move back, hit them, and then not need to breakaway again? That's not AS bad, I suppose.