Longstreet gets a lot more credit for his generalship; unsurprisingly, the Lost Causes absolutely loved trying to find a way to blame every single problem the Army of Northern Virginia had on him, and attributed all of his successes to others. Odds are, his reputation ends up being at least equivalent to Jackson's, especially since if he died from being shot during Wilderness their deaths would eerily parallel each other (both hit by friendly fire during battle, and in roughly the same battleground).
Also, post WW I his reputation will probably go up further, since he was one of the first generals to seriously push the idea that changes to military tech were starting to give a huge advantage to the defensive, emphasizing the value of entrenchment, etc.
Of course, without Longstreet the next question is who the Lost Causers blame for Gettysburg and other reversals of the ANV. A.P. Hill seems a likely candidate to me; assuming his death in battle isn't butterflied away, he won't be able to defend himself. The fact that he definitely did a poor job of making the transition from division commander to corps commander, and he caught a fair amount of flack from the Lost Causers in OTL contributes.