Q: FBI vs. police in sting operation

While almost anything is possible depending on the specific circumstances, I'll try to provide you with the most likely scenarios based upon the facts you've presented.

The FBI would not likely intervene, or take over, but would participate in a cooperative investigation since both agencies have a vested interest (concurrent jurisdictions) in successfully solving the incident case (murder) and getting a conviction in the subsequent prosecution.

For example: If the FBI's original case was RICO (Racketeer Influenced and Corrupt Organization) oriented, this case and any prior related cases may constitute predicate cases that support the RICO approach. The scale of a cooperative investigation may be of any size, from a pair of investigators from either agency teamed up as partners to a multi-investigator ad hoc task force; the potential scope of the investigation would be a consideration.

Since it is a case of concurrent jurisdiction, the prosecutors involved (US Attorney & state/county District Attorney) would coordinate prosecutorial efforts, and determine in which jurisdiction the perpetrator should be first charged/tried. That determines which agency makes the initial arrest. For example, if the defendant is to charged/tried by the state, he enters the state judicial system. The FBI, with approval of the US Attorney, can seek a warrant based upon sufficient probable cause (in the federal case) and subsequently have a detainer letter (notice of the outstanding federal warrant) filed (by the US Marshal) with whatever state detention facility in which the subject is housed. (Pre-trial release essentially becomes a moot issue; if he makes bond on the state murder charge--however unlikely--he goes into federal custody pursuant to the outstanding warrant.)

Both LE agencies would be interested in getting the subject to roll over against the higher-ups in the criminal organization. The crafting of any such deals (and relative terms) would be at the discretion of the involved prosecutors, not the involved LE agencies. They will assuredly be involved in that process, but most likely limited to making recommendations and/or offering opinions.

https://en.wikipedia.org/wiki/Racketeer_Influenced_and_Corrupt_Organizations_Act

Only in the movies or TV does the FBI "intervene" in anything. Local and Federal agencies work well together in real life, and nobody hides anything from the other. In many cases, locals are happy to have the Feds take over all duties, they're already stretched thin on money and people.

Jeff

Assuming the arrested person, having been suitably advised (Miranda rights) and subsequently waives those rights and elects to make a voluntary statement/answer questions/be interviewed regarding his involvement in the case, the involved investigators may suggest the possibility of a deal--however, they do not have authority to make/craft any such deal. That is solely at the discretion of the prosecutor.

Deals, as such, can be made at any time up to the moment the case goes to the jury (or the judge if there's no jury) for deliberation.

Federal agencies do not comment on ongoing investigations or court proceedings. There are exceptions; prosecutors, attorneys general, etc. Most state and local agencies follow suit. Deals struck in the course of the investigation/case would not be disclosed until so revealed to the court on the official (public) record. At the discretion of the court, that record (or part thereof) may subsequently be sealed.