Although this may seem like a topic put to rest a long time ago when he was explicitly referred to as Super Gogeta in the games and by characters. The fact remains that fans have argued about the true transformation in the movie Fusion Reborn for close to a decade now. Here’s both sides.
The side for Gogeta being SSJ:
We all know and love the SSJ 2 transformation by its give away blue aura, the animated blue lightening around the character is a conspicuous enough sign for viewers to distinguish between different transformations done by the Saiyans. Super Gogeta very obviously does NOT have these distinctive flashes around him, which is what most fans use to back their argument up.
Another point would be that in the movie Gogeta never had to go beyond SSJ to defeat Janemba in the first place. It was easy enough to defeat him in an SSJ state with Goku and Vegeta’s combined strength.
The case for Gogeta being SSJ2:
Other fans argue that Toei animation (the studio that produces DBZ) has on multiple occasions messed up in the past when it came to distinctive SSJ2 transformations (and a lot of other factors too actually), so the lack of blue lightening can’t essentially be relied on as a tiebreaker here. Only the creator Akira Toriyama has been consistent enough with transformation styles in the manga and as Fusion Reborn was a side story not based off of manga chapters we can never really know for sure.
Besides this, the hair for super Gogeta is actually immensely spiked and stiff, bearing a close resemblance to the hair sported by Goku and Gohan respectively in SSJ2 modes. Personally I believe too that the character design bears an uncanny similarity more to SSJ2 art than SSJ.
But it’s still up for debate, since we might as well never know for sure unless it’s from manga appearances.