Some camera review sites will test "shutter lag" and shot-to-shot times, and those specs may be helpful in measuring what you're concerned with.
However, assuming that newer technology will speed shutter lag is not necessarily a good assumption to make. There are quite a few different factors at work that can delay the time from shot-to-shot and some of these affect even dSLR shooters, and not all are surmountable by advancing processor or sensor technology.
Achieving autofocus lock is one of the main factors in shutter delay, as some cameras are set not to trip the shutter until focus lock is achieved. If you try and forego autofocusing, chances are very good you will have a blurry picture. And the time to acquire focus varies, depending on lighting conditions, whether the subject is moving, how closely the lens is already set to the focus distance needed, how fast the lens elements can be shifted, etc. This is not a constant. And even dSLRs have a hard time acquiring focus in low-light conditions. If you want to minimize this time, shooting in good light, controlling where the camera focuses, and setting the focus point or prefocusing using the shutter button half-press before taking the picture can help.
Another issue is how fast data can be read off the sensor and onto the card. This can depend on the write speed of the card, the size of the buffer in the camera, and how data is read off the sensor by the processor. And the higher the resolution of the sensor, the more data there is to shuttle around.
Another factor is that when the image sensor is also used for metering, that's another task that has to be performed and finished before the shot can be taken. This requires a lot of calculations, and the more data there is to chew through (again: think how much higher sensor resolutions have gotten), the longer this takes.
Another factor is that when the image sensor is also being used to feed the liveview on the LCD on the back of the camera (or in an electronic viewfinder), the charge from that data must be cleared from the sensor to avoid image ghosts appearing in the taken image.
Automated modes are also going to take more time than full-manual ones, because the camera typically has to gather some sort of data, and process it to make a setting, whether it be ISO (which setting is optimal?), white balance (finding out the color temp of the sensor data and then adjusting/shifting it), exposure (evaluating the light/dark values of the sensor data and then adjusting to place things along the dynamic range appropriately and by which settings), or focus.
Choosing a preset white balance, pre-focusing, and setting the iso, aperture, and shutter speed manually, may help speed things up a little, but since focus hunting is likely to be the largest possible delay, simply pre-focusing is liable to yield you the most speedup.
But compact digital cameras are nearly always going to have shot delays of some kind. If you really want to get around this, using a dSLR instead might be your best choice, budget allowing.