The populated token will be a 4/4 Dragon permanently.
The token will be whatever it was before. Copy effects copy base characteristics plus the results of other copy effects, and Dragonshift isn't a copy effect. At no time will the populated token be a 4/4 Dragon.
706.2. When copying an object, the copy acquires the copiable values of the original object's characteristics and, for an object on the stack, choices made when casting or activating it (mode, targets, the value of X, whether it was kicked, how it will affect multiple targets, and so on). The "copiable values" are the values derived from the text printed on the object (that text being name, mana cost, color indicator, card type, subtype, supertype, expansion symbol, rules text, power, toughness, and/or loyalty), as modified by other copy effects, by "as . . . enters the battlefield" and "as . . . is turned face up" abilities that set characteristics, and by abilities that caused the object to be face down. Other effects (including type-changing and text-changing effects), status, and counters are not copied.
Doesn't Dragonshift change the copiable characteristics of the token, meaning the populated token would be a 4/4 flying dragon?
Okay, now I'm not sure who's right. I know both Rhad and Epoch are gurus here, but now things are getting just a little too complex for me to be certain.
On some further consideration, I'm sticking with my originally accepted answer. There is no text on a token, that I'm aware of.
On further further consideration, I'm an idiot. I've got a lot of people telling me it's Rhad's way, so.. okay.
I initially thought the same thing, hunter9000, but I found this ruling on populate:
The new creature token copies the characteristics of the original token as stated by the effect that put the original token onto the battlefield.
The term in Dragonshift is becomes. Giant Growth doesn't say target becomes a 3/3. So, anything that has been Dragonshifted is a 4/4. Not a 2/2 +3/+3 =5/5 Bear Cub A dragonshifted bear cub with giant growth is a 4/4 +3/+3 = 7/7 Blue/Red Dragon with Flying. So wouldn't the original token also be a 4/4 Flying Dragon token?
No. As per the rule Rhadamanthus quoted, P/T-changing effects are not taken into account when copying a creature. They are not part of that creature's base copiable values.
This question was answered half a year ago, by the way.