So these are the species mentioned in the document as present in US zoos:
Tragelaphini
Common eland (195 in 23 institutions)
Giant eland (69 in 4 American and 2 non-American institutions)
Greater kudu (281 in 41 institutions)
Lesser kudu (128 in 19 institutions)
Sitatunga (92 in 10 institutions)
Mountain bongo (130 in 38 institutions)
Lowland nyala (151 in 20 institutions)
Antilopini
Southern gerenuk (51 in 11 institutions)
Springbok (79 in 9 institutions)
Addra gazelle (183 in 21 institutions)
Cuvier's gazelle (38 in X institutions)
Grant's gazelle (57 in 12 institutions)
Red-fronted gazelle (41 in 2 institutions)
Soemmering's gazelle (58 in 8 institutions)
Speke's gazelle (61 in 8 institutions)
Slender-horned gazelle (85 in 9 institutions)
Thomson's gazelle (207 in 20 institutions)
Madoquini
Guenther's dikdik (1 in 1 institution)
Kirk's dikdik s.l. (32 at 17 institutions)
Raphicerini
Steenbok (26 in 5 institutions)
Oreotragini
Klipspringer (45 in 18 institutions)
Reduncini
Waterbuck (Defassa and or Ellipsen?) (259 in 15 institutions)
Nile lechwe (232 in 10 institutions)
Red lechwe (31 in 3 institutions)
Uganda kob (34 in 2 institutions + unknown number in 3rd institution)
Alcelaphini
Bontebok (74 in 18 institutions)
Jackson's hartebeest (7 in two institutions)
Common wildebeest (230 in 22 institutions)
Hippotragini
Roan antelope (140 in 10 institutions)
Sable antelope (103 in 12 institutions)
Addax (220 in 24 institutions)
Arabian oryx (100 in 10 institutions)
Fringe-eared oryx (39 in 4 institutions)
Gemsbok (102 in 10 institutions)
Scimitar-horned oryx (242 in 18 institutions)
Cephalophini
Black duiker (21 in 7 institutions)
Blue duiker (51 in 17 institutions)
Red-flanked duiker (24 in 10 institutions)
Yellow-backed duiker (98 in 35 institutions)
I thought there were also still Royal antelope, Common duiker, Impala, Blackbuck and Nilgai in US zoos and Grey rhebok in a private center.
What about White-tailed wildebeest?
Species not in Europe zoos or only in remnants: Giant eland, Grant's gazelle, Red-fronted gazelle, Slender-horned gazelle, Grant's gazelle, Speke's gazelle, Soemmering's gazelle, Guenther's dikdik, Steenbok, Fringe-eared oryx, Bontebok, Black duiker, Southern gerenuk, Red-flanked duiker, Yellow-backed duiker, Uganda kob, Jackson's hartebeest & Klipspringer.
European zoos seem to have slightly less diversity but larger populations of many species. (sub-)Species present in Europe but absent in US: Blesbok, Beisa oryx, Kaama (1 left), Mountain reedbuck, Goitered gazelle, Kafue + Black lechwe, Black-faced impala, Dorcas gazelle, Natal red duiker. Also present in good numbers in Europe but not mentioned in these slides: White-tailed wildebeest, Impala, Blackbuck, Nilgai.
Overall US zoos seem to have higher diversity but lower numbers. If the sheet is complete for Wild sheep and goat Europe outperforms America clearly both in population size and species numbers (Alpine, West-Caucasian, East-Caucasian, Siberian, Nubian and Iberian ibex are kept in Europe for example).