Generally speaking, a physically smaller cap with the same voltage and capacitance is likely to have worse specs in other areas.
Is the new cap 105C or 85C? They typically operate in a warm environment.
Another important rating is ripple current. The smaller cap is likely to have a lower rating.
However, in most cases this cap is, relatively, under lower stress than other caps (especially for 220V operation), so it may be OK.
I had to replace a pair of calls in my oscilloscope. The original caps were unobtainable. The replacements we physically smaller. I do note a slightly higher amount of residual ripple, but it's not significant.