To put this into perspective....picture a 100 meter dash between an 18 year old athlete (a brand new Integra) and an 86 year old man (an Integra with 250,000 miles on it). Obviously the old man isn't going to school the kid...but he still may make it to the finish line. The Integra is pretty damn reliable and your B18B1 might last you to 300,000 miles...but age is age and with age comes the fact that things are going to break/not work as well as they should.
What model is your dad's Accord? Accords and Integras aren't exactly a great comparison...they're worlds apart in terms of engines (power and torque) and weight of the car. Accords generally have a little bit more torque than Integras do. I'm assuming your dad either has an F22B1 (EX Accord) or an F22B2 (DX, LX, etc Accord) since you said its fairly "close" in power to your motor.
Have you always kept up on maintaining the car as long as you've owned it?
Do you know how well previous owners took cars of it?
Are you up-to-date with tune-ups?