A bespoke solution will be perfectly fitted to your requirements (if you are lucky and skillfull) but expensive. If you are unlucky you will pay a fortune for something that does not fit your requirements or for something that is not well made or fit for purpose. So to ask for technical strenghts of a bespoke solution, since it could do anything, is non-sense. Its simply going to be as good as your developers, analysts, managers and finances allow.
What Alfresco will bring is a system that works for most people, built by experts in their field over several years, the advantages are cheaper costs for you and less risk but if your requirement is very specialised then a bespoke solution may be what you need.
You could also consider a hybrid solution which is to use a system such as alfresco and extend it with your own bespoke extensions if you have special requirements which is probably what most people will do.