This is one of those good questions. This is how I view it. The answer depends on what the driving force or what makes the reaction take place. This could be part of a general reaction of three-membered rings. A cyclopropane is rather more resistant to opening. An aziridine can open especially if aided by a leaving group. An epoxide can open under nucleophilic conditions or electrophilic conditions. If nucleophilic, then the nucleophile attacks as the least substituted carbon. If electrophilic, a weak electrophile is unable to open an epoxide directly. If the epoxide is treated with an acid, opening will now occur under a more SN1-like center. The nucleophile will attack the more stable carbocation "intermediate".
A chloronium or bromonium ion is similar to the protonated epoxide in being a good leaving group. Water could attack at either carbon. The identity of the product should indicate whether the reaction is SN2-like or SN1-like. Are the electrons of water sufficiently nucleophilic to initiate an attack on the less substituted carbon? Do the electrons need more positive charge to effect its attack? It is the latter case, but it still does not seem to react as an SN1 mechanism. The reaction with cyclohexene gives the trans chloro or bromoalcohol. So, the net reaction is SN2-like with SN1 regiochemistry.
Interestingly, I searched for a reaction of 1-methylcyclohexene oxide. Methoxide opens it with opening at the less hindered side and trans-diaxial opening. Under acidic conditions, I saw a Professor Wamser reporting methanol opening the epoxide to give the 2-methoxy-2-methyl-1-cyclohexanol of trans opening and with ethanol give a mixture of cis and trans I don't know the actual product, but I could imagine either.
This can often be difficult to predict very well. I think that if there is a neighboring pair of non-bonded electrons, they will always react with a carbocation faster than any rearrangement. That would be consistent with a lack of rearrangement of bromination or oxymercuration reactions. The non-bonded electron of bromine or mercury react faster than bonded electrons of a hydride, for example. That is why oxymercuration reactions do not give rearrangements while simple acid catalyzed hydrations may.