Both were very large, both contained a multitude of different people and cultures.
2.Both were victims of their own success, that is they looked rich and looked very good for invasion when weak, and both in the end were destroyed by invaders from outside at times of strife.
3.In the end they both tried to reach too far and were stopped, in case of the Achamanids they invaded the Greek states, had huge problems in maintaining their invasions and supplying their forces, naval or land based. The same is for Romans when they were stopped by the Parthian “Persian” Dynastie, See battle of Carrhae. The Romans had no sea route to Persia and had to cross large tracts of land, their armies at the end of extremely long supply chains were defeated. And a lot of the time all the Persians had to do was cut of their supply routes, see the campaigns of Julian, or Mark Antony.
4.Both had great impact on their people’s lives and culture, be it religiously, linguistically or architecturally.  See the use of large domes in buildings, a construction system innovated largely during the Parthian era. Religiously we can see the impact of ancient religions of the Persians on romans and consequently on Christianity, for example see “Mithraism” and its perpetuation from Persia into Rome, the disturbing similarities with Christianity. E.g. Mithra was called a “Son” of great god, had a virgin birth, walked among the people for a while, cured the sick etc.. died, was resurrected and then ascended into the heaven. What is interesting is that all Persians and Iranians celebrate the ascendant into heaven every year on March 20th which is very close to Easter. Nowrooz, is also celebrated in the republic of Azarbiegan, Uzbekistan, Tajikistan, Afghanistan, all Kurdish states, and a number of other states. By the way the word “istan” which means “the land of” is the root word for the English word “State”.
