Windows XP, when it came out, was limited to something around 128GB. This was fixed in SP2 and SP3. Just make sure you are updated to the latest service pack and you will be fine.
Why would you think a larger hard drive would slow down your computer?
If your motherboard supports the 250GB hard drive it shouldn't have a problem with the 1.5TB; assuming you have the proper connections for the drive type. Some older motherboards have problems with capacities over 128GB (+-), but that doesn't sound like its the case here. Just make sure you are buying a drive that matches the specifications of the motherboard, e.g. there is no point buying a SATA3 hard drive if your motherboard only has IDE or SATA1 connectors.