This isn't a bad thing. If you're going to steal, steal from the best. Your health bar shares the same line as your stamina. As you get tired, you come closer to being KO'd. If you can manage to back off from the fight for a moment, your stamina will refill to the maximum amount of health you possess.
More stamina means stronger hits.
It also means you can take more hits from the enemy. Certainly this feature has been done before in boxing titles, but it's a nice touch here. My single biggest complaint about UFC is that it's just plain dull. Every single fight is exactly like the one before it, almost to the point of feeling scripted. Jabs and kicks are exchanged for three to five seconds.