The 10th LA that you refer to is the 10th Battalion, Louisiana Infantry, otherwise known as the Yellow Jacket Battalion. They were almost exclusively formed from residents of St. Martin Parish (located in the extreme lower portion of Louisiana) although exceptions did occur. That seems to be a possibility with the Wilkerson/Wilkinson brothers as they both list Rapides Parish as their residence when they are with the 6th LA Cavalry (located in the middle of the state). It is entirely possible that they were both members of the two organizations.

There is a short history of both the 10th Battalion and the 6th LA Cavalry in Dr. Arthur W. Bergeron, Jr'.s "Guide to Louisiana Confederate Military Units, 1861-1865". Their service records are available in A. B. Booth's "Records of Louisiana Confederate Soldiers and Louisiana Confederate Commands" and listed below. (These are probably the ones you saw online).

Wilkinson, E. G., Pvt. Co. -, 10th Battn. La. Inf. Federal Rolls of Prisoners of War, Captured
East Baton Rouge, Nov. 25, 1864 (so on Roll). Paroled for exchange at New Orleans, La., Aug. 21,
1865. Exchanged near Red Wood Creek on the plank road, between Baton Rouge and Clinton, La.,
Aug. 22, 1864.

Wilkinson, G. W., Pvt. Co. A, 10th Battn. La. Inf. Federal Rolls of Prisoners of War, Captured
Bayou Teche, La., April 14, 1863. Sent to New Orleans, La., to be exchanged April 27, 1863.