Regardless of which one you pick it would be cool if you competed with the other agency in a space race and this could affect funds and reputation.
Losing a world first to the rival agency should lower your reputation somewhat, though not as much as failed missions or dead kerbonauts, in an effort to recreate the space race feel of the 1960s. This would create extra incentive for the player to do things quickly and add an interesting new dimension to the game where you aren't the only space agency on the planet.
There could be so much flavor added with this too. For example you could have a policy where you encourage your leader either, JFKerbal, or Nikita Kerbchev, to make a "Go to the Mun" speech which will give certain benefits but have major reputation and maybe funding repercussions if you fail to meet the deadline or the rival agency beats you there.
There are other potential characters like Lyndon B Kerbson and Sergei Kerborolev. (really like these names lol)
There are lots of other good quotes too.
"What can we do, how can we keep up?" - JFKerbal
"I believe that this nation should commit, before X, of landing a Kerbal on the Mun and returning him safely to the Earth." - JFKerbal
"Would you rather us be a second-rate nation or should we spend a little money?" - Lyndon B Kerbson
"Control of space means control of the world." - Lyndon B Kerbson
"Whether you like it or not history is on our side. We will bury you!" - Nikita Kerbchev
Some others
"We don't know anything about it, we are all asleep down here." - NASA Administrator Reponses to reporter calling about Yuri Gagarin at 3 AM
"The gap is not closing, but increasing!" - Pravada 1960s
