They are very different experiences, though I'm pretty sure there is excellent teaching to be had at both and in the end you will have to make your own decision based on travelling time, cost, other family members and "gut feeling" . Caveat: my experience is limited to one DS who attended CHB for sixth form, and to friends with children at both places over the years.
SolSch is dripping with money and the facilities show it - music block, concert hall the envy of the Borough, lots of other new building, exotic overseas trips, glossy brochures. Many (though by no means all) of the parents are also well-heeled, fairly local, regular supporters of school functions etc. Lots of long-standing family attendance over generations. Some feeling that some of the teachers lower down the school are not yet fully au fait with the ways of girls but integration seems to have been smooth enough -the first cohort of 11+ girls must be just about to leave the 6th form. Leafy (if busy) location close to Solihull Hospital and to the delights of the Touchwood shopping centre. Sport is often seen as one of its strengths.
CHB in contrast feels as if there is far less money sloshing around, and the buildings are much less impressive (although the site has its own share of leafiness by the park). The intake is far more varied ethnically, financially and geographically, with some travelling very long distances. Facilities can feel cramped and maybe Kings Heath High St has fewer temptations than Solihull town centre? There is still plenty going on though, and the music for example benefits from the participation in Birmingham's Music service (assuming that hasn't been cut to shreds).
Solihull School will cost tens of thousands of pounds over the years, even with scholarships, and will no doubt ensure your son emerges well-rounded and confident. I have not always been impressed with tales of 6th form advice there, and (like many schools) it can exist in rather a bubble: spending those tens of thousands will not necessarily ensure A*A*A* and an Oxford place, or even the best advice about other options. However if money is not an issue, and you mix socially with people for whom money is not an issue, and it is close enough for easy travelling to friends etc, then why not enjoy all the benefits you and previous parents have paid for?
If money is tight, and you live within reasonable travelling distance of CHB, it would seem a shame to turn down one of the best free educational experiences in the region, unless there are other good social or family reasons for SolSch. However both places will I'm sure attempt to push their pupils to achieve: CHB regularly tops the exam and university entrance tables and my DS2 thoroughly enjoyed his 2 years there and was certainly intellectually, musically and socially stretched.