We know that the first ten people who make up a minyan get schar for every person who attends that minyan. So what happens if a person and their father come to shul and see that there are 9 people. Should the son try to be before his father so that he gets the schar, or should he let his father go first in order to honor him and not get schar?
My answer is based on what I found at ateret4u.com. This is from Rabbi Gamliel Rabinowitz.
In Siman 36 he asks a question whether it is better to be from the Asara Rishonim in a Shul where there is no Birchas Kohanim or to go to a Minyan where he will not be from the Asara Rishonim yet will get Birchas Kohanim.
In the discussion he discusses whether it is more important to go to Shul wearing Talis and Tefilin already or to be from the Asara Rishonim and put on Talis and Tefilin in Shul. He brings a dispute regarding this with many who prefer the former and many that prefer the latter.
In conclusion to the Birchas Kohanim question he concludes that it would be preferable to get Birchas Kohanim over being from the Asara Rishonim.
Based on the above I would conclude that the Mitzva of Kibud Av is definitely more important than being from the Asara Rishonim.
R. Bentzion Abba Shaul rules in such a case that one should allow the father to be the tenth member (Ohr LeTzion vol. 2 §22). His argument is simply because one is obligated to respect his father.
However, this may not be in agreement with all authorities for a couple of reasons:
- Some maintain that in matters of commandments, the dictum "respect isn't accorded to a teacher on account of respect for God" (אין חולקין כבוד לרב) overrides other obligations; see Shaarei Teshuvah (OC §658).
- A recognized standpoint regarding the obligation of honoring a parent is that when there is no direct, personal honor done for the parent one is not obligated to do the task in question (cf. Ramban Yeb. 6a s.v. Ma le'hanach, Tosafot Kid. 32a s.v. Rav Yehudah).
You assume that giving the reward of being one of the first ten constitutes honouring parents.
A) Halachipedia quotes the parameters of honour as follows:
Honoring One's Parents
- Included in honoring one's parents is feeding, dressing, and helping them walk. When one is doing such an activity, one should do it with a smile. 
Standing for One's Parents
One must stand before one's mother and father unless they forgo this honor.
One should stand for one's parent once he enters one's eyesight.
According to Ashkenazim one only needs to stand once a day and once a night. According to Sephardim, one should stand every time a parent enters the room even if it is a hundred times a day.
Honoring in Thought
- One must honor his parents in thought as well. One should imagine that his parents are the most important people in the world even if other people do not see it that way. 
Spending Money on One's Parents
- Even though the cost of fulfilling the mitzva of kibbud av va'em is supposed to come from the parents money, if the child chooses to pay, it is considered a mitzva. 
B) Extracted from a shiur by Rav Mordechai Willig are these words on the parameters of honouring parents (=kav"a)
What is kav"a while parents are alive? The Gemara writes that honoring includes giving food and drink, dressing and covering, and escorting in and out. Apparently, the Ri Hazaken and Maharsha interpret that kavod does not mean "honor" in the classical sense, but rather service.
From these sources, it seems that the mitzva of honouring parents is not technically fulfilled by letting the father be one of the first ten and so the son may, if he wishes, go first.
It could be that the father would be most honoured by seeing the keenness of his son to get the reward of being one of the first ten. But if he would not, maybe the son should forgo the reward in order to foster a good feeling between them.