It depends why you are comparing them. If you are playing top trumps in the pub then BHP (PS) is a good measure of an engines peak output. However, this doesn't tell the whole story.
Power to weight ratio is a good measure of how an actual vehicle will perform but again, it doesn't tell the whole story.
Essentially, if you are looking to compare just one engine against another, peak power is one measure you can apply. If you are comparing one vehicle against another, power to weight ratio is a better measure but is still flawed.
It all very much depends on what you are comparing vehicles for.
With regards to purely measurable engine data, you have another number which may give you more information about how tractable an engine will be; Torque, typically measured in Netwon Meters or Foot Pounds. In simple terms, peek power is how fast you will hit the wall but torque is how far you will carry the wall with you.
Neither of these figures in isolation, even if you know the point in the rev band which each occors still doesn't tell you the full story. For that you need to look at the actual power graph. An engine with lots of volume under the graph will be more tractable. For example, an engine which makes 80% of it's peak power at 1500 RPM and continues delivering at least that number up until the red line will be far more tractable than an engine that delivers more peak power but doesn't deliver any appreciable power until say 5500 RPM.
When it comes to a specific car, you can't simply compare like for like vehicles with different engines because you still have to consider gearbox radtios, final drive ratio, etc...
You also can't use power to weight as an absolute measure because you also have to consider weight distribution, powered wheels and handling characteristics such as centre of gravity, suspension articulation, track, camber, yaw angles, etc, etc...
If you want to compare two cars, your best indicator is lap time on a known track with the same driver on the same day with the same weather conditions but this again doesn't cater for things such as different tyres, etc...
If you want to compare two known cars that you have available, the best advice is to drive them.