APC Smart UPS - 2700uF 40V Capacitors
Surely a 2700uF 40V cap is still a 2700uF 40V cap no matter how big it is


No. Those are only two of the important parameters that define electrolytic capacitors.

The others are: maximum operating temperature (which can have a huge impact on life), loss tangent/DF/Q, ESR, and (as @Unimportant stated) the ripple current rating.

Capacitors are always improving and getting smaller, so it is possible your new ones are suitable. But you will need to get the datasheets for both and verify this.