[...] the new Nikon bridge camera the P510.
Niice. But easy to achieve sharp images these days with any camera, in normal lighting conditions. If you want a versatile camera for different (natural) lighting situation and creative approaches you need to consider a few other things such as speed of glass, sensor size, etc. If you want to avoid flat or unflattering images through flash you need to consider a few more things. Note I write this based on my shooting style and preference, which differs for all of us.
For the type of shots you make and your preferred style of shooting (and those are assumptions based on what I see here :-) ) and assuming you dont want to use Flash and have some sort of manual control, the OMD may be the best choice. It has the best combination of performance metrics (sensor, AF, IS, etc.) and with say the standard zoom that comes with the body and the Panasonic AF 25mm 1.4 you'll be ready to rock in pretty much any situation.
Use the zoom for travel shots at around f/2.8-5.6, use the 25mm for bar and in-room (50mm equivalent). When you shoot the 25mm set it to auto ISO, auto-WB, max IS, set shutter speed to 1/60 (or 1/125 if you're shaky) and shoot wide open at 1.4. Focus on your target first by half press shutter button, then compose keeping the shutter button half pressed and then fire when you're ready. Change the distance between lens and subject to play with DOF. The outcome is the best you will be able to achieve with any set up given natural light conditions, unless you also crank up the ISO to max also. If the model is dark and the background light crank up the exposure compensation to +1-ish to balance your shots contrast and exposure.
There is another route to optimizing performance on these types of camera's but that involves MF and ultra high speed glass, different approach.
If you want to shoot full auto everything, one zoom lens, with flash, the X10 you have is lovely, arguable the best compact around, you can get a lot out of that one.
Again, ultimately depends what you want, how you want it and more importantly what you do with any camera you use.