Hemiepiphyseodesis ( ill shorten to HE) and corrective osteotomies are both methods used to correct deformities in bones.
Corrective osteotomies involve making cuts in bones and either removing or inserting small triangular wedges of bone ( closing and opening wedge osteotomy) respectively, this then effects straightening of prior deformity.
The advantage of this method is a fast correction which can be achieved in a single operation.
The disadvantage is the complications associated with a major surgery such as bleeding and excessive pressure buildup in the legs. These are however usually uncommon in in the hand of well trained hands. There is also a risk of recurrence which is a major problem especially when used in the treatment of Blounts disease.
In contrast HE is method that surgically guides growth at the deformity area by applying materials on one side of the bone(hence the word hemi) which reduce growth on one side of the bone and so as the child grows the deformity prgressively corrects.
The advantages are that it is associated with less pain, shorter immobilization, decreased cost, and less surgical risk.
It however has the following known complications like stunting of growth on side of application ,a rebound period unitended increased growth at application site. It is also like I said earlier a slower method of correction compared to an osteotomy useful only in patient who still have some time of growth left.
Its difficult to say which method is better as a generalised statement the choice usually boils down to severity of the deformity, cause of deformity , the expertise of the doctor and how long is available for the correction, we also balance the merits and demerits of each procedure in consideration with the patient/ guardians.
I suspect the options were given you by a trained paediatric orthopedic surgeon and armed with more information you and your doctor can decide on the method best for your child. All the best.