The answer to this question falls to what state or municipality is charging, and what the local or state laws are. Aggravated assault has a wide range of meaning, so if you could be a tad more specific, I could give you a better answer.
In a general sense, the "aggravated" is a more serious charge of assault. The aggravation could stem from the use of a weapon, to being under the influence, and a host of other mitigating and exacerbating factors in between.
vvv That's not true, Steve. In Arizona, the maximum sentence for Aggravated Assault is up to 21 years with current sentencing guidelines. New York has varying "degrees" of Assault, and sentences range from 1 to 25 years. Texas is 2 to 25 years. The wide variation in definitions and sentences is why I asked for clarification, else we'd be typing out a huge list of state-by-state definitions and penalties.
There is certainly a statute of limitations for most felonies in California, as there is in every other state of which I am aware. The usual time limit is 3 years, though it is longer in many cases.
However, the statute is a limitation upon the COMMENCEMENT of a criminal proceeding, not on bringing somebody to trial If an arrest warrant was issued for this person, then the proceeding has commenced and the statute of limitations has been satisfied under CA law. (Pen. Code sec. 804.)
If a proceeding had not been commenced, the time for doing so could be "tolled" for a period of time while the person was out of the state, but that "tolling" is limited to a maximum of three years. (Pen. Code sec. 803.)