The two bills [SB 229 and SB 975] are identical and each is taken virtually verbatim from the federal RFRA (42 USC 2000bb et seq). The Arkansas bills simply change the references to federal law to refer to state law. The new versions do require that relief can only be granted against the government (removing the private vs. private problem) and eliminates the extremely broad "compelling interest" language to conform to the conventional legal terms.
The law does not really fix the problem of potential discrimination however. Of course, Arkansas does not have any statutes that protect LGBT folks from discrimination at all so it is perfectly legal to fire or refuse to hire people, deny them business services, refuse them housing etc on the basis of their sexual orientation or gender identity. Thus, the state RFRA changes nothing in that regard at the moment. However, if the state added LGBT status to the state civil rights law, then the act could be used to claim an exemption from that portion of the civil rights laws. Although the Supreme Court has not spoken on this precise issue (does RFRA allow a person to exempt themselves from the coverage of civil rights laws), many state courts have said 'NO." See http://volokh.com/wp/wp-content/uploads/2009/12/elanephotographytrialorder.pdf for the leading state discussion canvassing all of the arguments and citing other, similar cases.
The new versions would still allow the county clerk to deny a gay couple a marriage license and then defend his or her actions using RFRA. The trick is whether or not the clerk could use it as a defense to suit brought by the couple seeking to force the issuance of the marriage license or as a defense to some adverse employment action.
Finally, the larger question (aside from elephant sitting over there in the corner - the lack of any legal protection for LGBT status) is why do we need a state RFRA at all? Religious Liberty is NOT under attack and does NOT need "restoration." No one is being forced to attend church or being punished for failing to do so. Everyone may believe, speak about and advocate for their beliefs. Religion seems to be alive, well, and prospering in Arkansas. What the proponents believe is that denying service to a gay person or couple is not discrimination. Until that issue is brought to the surface and decided - either by express statutory language or by court decision - then this "fix" simply kicks that can down the road.
One more thing: this language is in the Texas RFRA which was adopted in 1999: “This chapter does not establish or eliminate a defense to a claim under any federal, state or local law protecting civil rights or preventing discrimination.”
Why not include similar wording in the Arkansas version? I would cut out the words "or eliminate" but that's just me.