Using your own tissue to repair a torn ligament such as the ACL is called an autograft. Using tissue from a donor bank is referred to as an allograft. In either case, once the tissue is transplanted and in place, the graft dies.
This means the cells are no longer viable. It's the structure of the tendon that remains. This structure is called a collagen matrix. The body sends in blood vessels to destroy the old collagen in the matrix. The tissue is gradually replaced with new collagen cells. Living cells fill in along the matrix until a new structure is formed.
Many studies have been done to compare the results using allograft versus autograft tissue. Patients with allograft ACLs have reported slight deficits in knee flexion and pain behind the kneecap. Rerupture may occur slightly more often with allograft tissue when the graft is taken from the patellar tendon.
Otherwise, it appears that strength and activity levels are about the same with either type of graft. There may be a slight delay with less graft incorporation with allograft tissue. Some researchers suggest a delayed or prolonged rehab program for these patients.
With your own tissue, you won't likely experience this delayed remodeling and can progress through knee loading activities on schedule.