Any service where you don't park it yourself and hand the keys over has unfortunately got a poor reputation in recent times at Heathrow and elsewhere for vehicles being left in fields, supermarket car parks, used as runabouts by staff, even getting parking tickets. I'm sure the mainstream operators are dismayed at all this, but if you do use such a service record the mileage on handover, take one with you and leave another prominently in the car.
The Underground generally provides a better T3-T5 transfer. The trains are more frequent, every 10 minutes maximum instead of every 15 on the HEx, and the stations are nearer the terminals. You need an Oyster or Contactless card to get in and out, but they don't charge you for internal Heathrow trips.