Is the die of SMD transistors different from die of DIP transistors with a unique part number?
Is the power transmission of a transistor dependent on its package type or chip type ?
Assuming you're asking about the die, then parts with the same part number from the same manufacturer will typically have identical dice inside regardless of what package they use. There's no rule that says they have to, though; they could use specially-designed dice to fit more conveniently in different leadframes if they had reason to.
Economically it makes more sense to use one die design for multiple packages, however, if that's an option. Engineering a semiconductor die is not a trivial task, and has a lot of up-front cost associated with it, from paying the engineers designing it, to producing the photomasks for constructing it, to having to change tooling between runs of the two different types.
The package is typically what determines power dissipation. Packages that do a poor job of extracting heat (for example, TO-92 or SOT-23) will support a much higher temperature difference between the die and the ambient air, as the plastic they're made from is a thermal insulator. Packages like TO-220 or SOT-223, on the other hand, have a dedicated terminal that's thermally bonded to the die and that provides a path to conduct heat outside the package and to a heatsink.