Both injury completeness and level can impact bowel and bladder function, but your question mostly has to do with level of injury. Injuries above the conus medullaris (upper motor neuron injuries) would cause bowel/bladder spasticity. Injuries distal to the conus medullaris (lower motor neuron injuries) would cause flaccidity.
Individuals with incomplete spinal cord injuries likely have more strength and sensation – and therefore fewer bowel/bladder problems than individuals with complete SCIs.