Another comparison:
A320 OEW (CFM56): 42.1
Range with 150 pax: Up to 3090NM
Max pax: 180
B737-800 OEW: 41.1
Range with 160 pax: Up to 2940NM
Max pax: 189
Not much of a difference, but coupled with a slight pax disadvantage.
A321 OEW (CFM56): 47.9
Range with 185 pax: Up to 3000NM
Max pax: 220
B737-900ER OEW: 43.4 (est, Boeing claims it'll be "4536 kgs lighter than A321")
Range (no pax info): 3200NM
Max pax: 215
If Boeing keeps it word, rather a sizeable difference. Slightly fewer pax, but more range.