The Boxer is the more demanding of the two on exercise, at 5/5 against 4/5, and its energy is famously durable — this is a breed that plays like a puppy at seven.
What satisfies it is an hour and a half of varied activity: walking, off-lead running where safe, play with other dogs, and training. At 4/5 trainability it does well in obedience, agility and scent work, and the mental component genuinely helps because an under-occupied Boxer is a bouncing, mouthy, demanding presence in a house.
The shortened muzzle limits it, though. Boxers overheat faster than a normally muzzled dog and cannot be run hard in warm weather. That combination — high exercise need and low heat tolerance — means summer routines have to shift substantially.
The Pit Bull's 4/5 is an hour to ninety minutes of largely physical work — a brisk walk plus a flirt pole, spring pole, tug or a training session — and it settles hard afterwards. It also tolerates warmth better.
Both breeds need their exercise built up gradually through the first eighteen months, since hip and elbow dysplasia sit on both lists and forced running, stairs and repetitive jumping on a growing joint are avoidable risks.
On cost the Pit Bull is the cheaper dog at cost level 2/5 against 4/5, $80–150 a month against $100–200, and $1,200–2,200 in the first year against $1,500–3,000. The Boxer's premium is partly size and partly the veterinary profile — cardiac workups, Holter monitoring, oncology and the higher insurance premiums that follow from both.
The Pit Bull's own hidden cost is insurance of a different kind: availability rather than price, since bully-type breeds are frequently excluded outright.