The Starfighter aircraft and the generic 1/500 sets from Gold Medal and Tom's should work fine. The Starfighter gun turret set would only be appropriate for a World War II-configuration Essex-class ship. (The only one of those on 1/500 scale is the ancient Lindberg one. The Renwal/Revell kit represents the ships in their 1960s configuration - which is, to say the least, dramatically different.) The Gold Medal aircraft carrier set is on 1/540 scale. I suspect a lot of the parts in it would look ok on a 1/500 model - but others probably wouldn't.
In re-releasing two old Essex-class kits at the same time, Revell is undoubtedly confusing a lot of people. Revell and Renwal used to be two competing companies. They both issued Essex-class kits in the early 1960s. Revell, if I remember right, was first. Its kit came out in a box labeled Essex, and represented the ship more-or-less as she looked at the time the kit was released - with the angled deck and much-modified island. It was on one of Revell's notorious "box scales" - about 1/540. The Gold Medal aircraft carrier set is designed for this kit.
Renwal's came out a little later, under the name Shangri La. (I think the box of the reissue is a reproduction of the original.) Like almost all Renwal's other ship kits, it was on 1/500 scale. (Renwal was an early pioneer in the idea of constant-scale kits.) It also showed the ship in her 1960s configuration. I have the impression that it was a little more accurate in some key respects - but less accurate in others. (As I recall, it had a flat bottom.)
Both kits got reissued several times over the years. Renwal went belly-up in, I think, the 1970s. (I spent a few minutes googling Renwal, but couldn't find a real company history.) Eventually the Renwal molds ended up in the hands of Revell, which has reissued some of the kits over the past couple of years.
Just this past month or so, Revell reissued two very different Essex-carrier kits. The one labeled Hornet is the old, 1/540 Revell version, with a few extra parts (including an Apollo space capsule) that were added for a reissue shortly after the 1969 moon landing. The one labeled Shangri La is the old 1/500 Renwal one. As GMorrison noted earlier, the scale of the Shangri La is about 10% larger. In terms of aftermarket parts, that may or may not make much of a difference - depending on the part and the individual modeler's judgment.
Personally, I'm glad those old Renwal kits are back. The military kits were great. (One exception: the included figures, which were some of the awfullest, zombie-like humanoids ever put in plastic kit boxes.) I'd also like to see the nice little 1/48 classic cars (each with its own clear plastic case) again. And who can forget the Visible Man - and the Visible Woman (with optional parts to make her pregnant)?
What I don't particularly want to see is the resurrection of the "AeroSkin" airplanes. Old timers will remember those WWI, pre-WWI, and '20s kits. They came with pre-printed "fabric," and the styrene parts featured wing and fuselage ribs molded in relief. The modeler stuck the paper to the styrene parts with a bottle of cement that came with the kit. (I think it was the same as Testor's bottle formula - mostly carbon tetrachloride.) The problem was that as the glue dried it distorted the plastic parts; your Sopwith Camel might look great in the beginning, but after a week or so its wings would warp into an arc of a circle. Ah, memories....