They should not be necessarily behind. To compare apples to apples, the nearest similar thrust to the PS-90A1 (171 kN) is the 30 years older CF6-6 (185 kN).
Comparing those two, the PA-90 has better specific fuel consumption in cruise, 0.595 vs. 0.646 lb/hr/lbf.
The A2 variant for instance was developed "in co-operation with Pratt & Whitney." If I had to guess, it's because the PS-90 fills a gap in the thrust range, gone since ETOPS put the tris and quads in decline. Nowadays the most common thrusts are 100-120 kN for the narrow-bodies, and the latest big jets are 350+ kN.
We haven't seen a twin-jet wide-body from Russia, say like the 777 or A330. If that day comes, and they decide to build an engine and not out-source it, then we can have a better comparison with what's available from the big three—GE, P&W, and RR—in the high thrust range.
The Aviadvigatel PD-14 is still in development, and it's in the 120 kN range. Wikipedia says its SFC is 0.526, which is comparable to the CFM56 (not the new LEAP model), I'm not sure how reliable that figure is, because the references linked don't show that figure, instead they say:
10-15% [improvement] relative to other contemporary engines of the similar thrust range and application.
And a geared-turbofan offshoot is planned, so they want to compete with the PW1000G.
Related: Why don't Russian aircraft sell as much as their European/American counterparts?