It really depends on the context of the comparison. If Steve means it in a way to encourage Tony to be more like Howard in positive aspects, like Howard's selflessness perhaps, Tony might initially be annoyed but then might see the point. However, if it comes across as Steve thinking Tony is lacking compared to Howard in general, it would be a big blow to Tony's ego and definitely harm their relationship. In the fanfiction world, this comparison could be a major plot device to drive conflict and character development.
Well, it could strain their relationship. If Steve compares Tony unfavorably to Howard, Tony might feel insulted and resentful. He wants to be seen as his own person, not just in the shadow of his father. This could lead to arguments and a rift between them.