There are different versions with the same name. Here's some info from the folk index:

Big Eyed Rabbit [Me IV-E 25]
Rt - Buck Eyed Rabbit
Uf - I Don't Love ('a) Nobody
1. Creed, Kyle; and Fred Cockerham. Clawhammer Banjo, County CD 2716/701, CD/ (2002/1966), trk# 19 [1964/10]
2. Davis, Eva; & Samantha Bumgartner. Banjo Pickin' Girl, Rounder 1029, LP (1978), trk# A.01 [1924/04/23ca]
3. Jarrell, Tommy. Joke on the Puppy, Heritage (Galax) 044, LP (1992), trk# 10
4. Ledford String Band. Ledford String Band, Rounder 0008, LP (1972), trk# B.01
5. Mainer, Wade. Old Time Banjo Tunes, Old Homestead OHS-90168, LP (1984), trk# A.05
6. Plank Road String Band. Plank Road String Band, Carryon, LP (1976), trk# B.05
7. Powell, Dirk. If I Go Ten Thousand Miles, Rounder 0384, CD (1996), trk# 9 (Brown Eyed Rabbit)
8. Reid, Bruce. Silberberg, Gene (ed.) / Complete Fiddle Tunes I Either Did or Did Not.., Silberberg, Fol (2005), p 12
9. Sutphin, Kirk. Old Roots and New Branches, County CD 2711, CD (1994), trk# 8

Big Eyed Rabbit #2
1. Slaughter, Matokie; and the Back Creek Buddies. Saro, Marimac 9028, Cas (1990), trk# 8
2. Slaughter, Matokie. Clawhammer Banjo. Vol 2 [More Clawhammer Banjo], County CD 2717/717, LP (2003/1969), trk# 3

Buck Eyed Rabbit [Me IV-E 25]
Rt - Shortenin' Bread ; Big Eyed Rabbit
10. Hopkins, Al; and his Buckle Busters. Fiddlers Convention in Mountain City, Tennessee, County 525, LP (1972), trk# 10 [1926/10/22]
11. Johnson, Arthur D.. Old-Time Banjo Anthology, Vol. 1, Marimac AHS 4, Cas (1991), trk# 17 [1987/08/12]
12. Pillans, E. H.. Lomax, Alan / Folksongs of North America, Doubleday Dolphin, Sof (1975/1960), p504/#266

Russian Rabbit [Me IV-E 25]
At - Hoosier Rabbit ; Bell Cow
Rm - John Brown's Dream
13. Fraley, J. P. and Annadeene. Wild Rose of the Mountain, Rounder 0037, CD/ (2000), trk# 14 [1972-73] (Rooshian Rabbit)
14. Hartford, John. Devil's Box, Devil's Box, Ser, 31/2, p14(1997) [?]
15. Salyer, John Morgan. Titon, Jeff Todd / Old Time Kentucky Fiddle Tunes, Kentucky, Bk/ (2001), p165/#139 [1941-42]
16. Salyer, John Morgan. Home Recordings 1941-42. Vol. 2, Appalachian Center Ser. AC 003-v2, cas (1993),