Carbocation formation in electrophilic addition of hydrogen halides to alkenes
The rate determining step is carbocation formation. After which, depending on conditions, the trapping of the cation may or may not be slow enough for [1,2]-shifts.

The [1,2]-shifts are probably under thermodynamic control if there is time for them to take place. This means that if there's time for the shifts, we're hunting for the most stable cation. Otherwise, you trap the most readily formed cation in a kinetic sense (which is not necessarily the most stable).

Assuming shifts are fast, I think your solution is better because the tertiary cation is more stable. Dichloromethane doesn't undergo substitution as easily as t-butyl chloride, so I would have to argue that the tertiary carbocation is more stable.