The P345 is nicely rounded on the front of the slide, while the P89 is merely squared off and beveled. The P89's sharp-cornered slide release is obtrusive, reaching outside the wider-than-it-needs-to-be frame, while the P345's has been de-horned and only hangs out about 0.125" outside the slide (compared to 0.20" on the P89).
The safety/decocker on the P345 is checkered for your fingers, while the P89's has lugs that hang out to provide a bearing surface. Also, the P89's safety has a corner that's a bit obtrusive when it's in the safe position; the P345's safety has been sensibly trimmed. Both guns are safe when the safety is down, and ready to fire when it's up. This is backwards to my way of thinking, so I'll call that a strike against both guns.
The P89 trigger guard is very heavy and has a hump on the front, while the P345's is slimmer and more streamlined. The P89 trigger is a bit rough and cobby in finish and is squared off on the edges, but the P345 trigger is well finished, well rounded, and has a more comfortable curve to it.
As I mentioned earlier, the internals of the P345 have been slimmed down when compared with the P89. They're still plenty beefy, though. The most noticeable difference is the guide rod. The barrel lacks a swiveling link, and the takedown pin goes through the guide rod instead.
The rear of the guide rod engages with the bottom of the barrel via some magical geometry, and there are two springs on the guide rod; one is a standard coiled wire spring, while the other, which no doubt acts as a recoil buffer, is made of sheet metal.