The review site you use is wrong in stating that the most important factor in gauging the performance of a lens is "image resolution in lines". That is a measure of LP/PH, or Line Pairs per Picture Height, and it is a common means of gauging lens performance, but by no means the best. It is quite simply the easiest.
Lens performance is appropriately measured via MTF, or Modulation Transfer Function. By using MTF, a multitude of factors about a lens's performance, from center to corner, can be gleaned. Diagonal sets of line pairs of increasing resolution are normally used when determining the MTF of a lens. The use of diagonal lines configured 90° perpendicular to each other allows more than simply the resolving power of a lens to be determined...it also allows optical aberrations to be discovered and their degree determined. Field Curvature can be determined via MTF as well.
Line Pairs per Picture Height is a sketchy measure, as lenses do not perform identically at the center as they do midway to the edge or in the corner. The LP/PH at the center of most lenses tends to be higher, and generally free of aberrations, where as LP/PH in the corner tends to be lower, sometimes much lower, and often riddled with aberrations. You can see this on something like an ISO 12233 chart, but accurately measuring actual resolution off such a chart anywhere but the center of the lens can be very difficult.
Many lens manufacturers provide MTF charts for each of their lenses. Canon is most well known for this, Nikon offers them on some of their sites. An MTF plot usually has two sets of curves in an X/Y plane, where the X axis represents radial position on the lens from center to corner, and the Y axis represents the resolving power. Canon MTFs have black and blue lines, solid and dotted, to represent performance at maximum aperture as well as at f/8, in both Saggital as well as Meridional angles (diagonals, 90° separated). According to the original basis for Canon MTFs, anything over 0.8 is "excellent", anything under 0.6 is "poor", anything between the two is "acceptable" to "good".
Most MTFs work the same way, although the specific nuances may differ. With modern sensors pushing the resolution envelope, one should probably expect more out of a lens. Personally, I consider 0.7 to be the threshold of acceptability in a Canon lens (should apply to Nikon as well), while I consider 0.9 to be the threshold of "excellent".
When it comes to sensor comparisons, things are a lot simpler. Sensors, from a resolution standpoint, provide consistent measurements from edge to edge. Sensor spatial resolution is best described in terms of either pixel pitch or a literal spatial resolution measure (lp/mm, or line pairs per millimeter.) One can derive this by dividing the width of the sensor in millimeters by the number of pixels wide. If a sensor has 6000 pixels on the x (width) axis, and is 36mm wide, then the pixel pitch is 0.006mm. Multiply by 1000 to convert to microns (µm)...in this case, the pixel pitch of a FF (36mm) sensor with 6000 pixels wide has a pixel pitch of 6µm. The basic formula for this is:
pitch µm/px = (sensorWidth mm / imageWidth px) * 1000 µm/mm
One can convert pixel pitch, which is a simple, scalar number that can be useful for comparison, into spatial resolution as well. Converting sensor resolution into terms of spatial resolution allows it to be compared with other things that can also be converted into spatial resolution, such as a lens' resolving power. Spatial resolution is most often expressed in terms of lp/mm, or cycles/mm (same thing for all intents and purposes). The formula is similar to that for determining pitch:
spatRes = (1 px / (sensorWidth mm / imageWidth px) * 2 l/lp
One can compare the resolving power of a camera by comparing pixel pitches or spatial resolutions. One can also use sensor spatial resolution as a basis for determining total "system resolution", the final output resolution of any given lens and camera combination, to compare how different cameras with certain lenses compare to each other (assuming you have an MTF for the lenses.)
It should be noted that more resolving power is not necessarily always better. In terms of "lines resolved", one can achieve the same LP/PH with a number of different sensors of differing sizes. One could easily produce the same image resolution (image dimensions, say 6000x4000 pixels) from a tiny compact sensor, a medium-sized sensor, and a full-frame DSLR sensor. The 24mp images from each will appear to "resolve" the same from an LP/PH standpoint so long as the subject is framed the same in each camera. There are other key differences between those sensors that a simple LP/PH measure simply cannot tell you. One example would be the simple fact that signal dynamic range drops as pixel size shrinks, which will lead to higher and higher levels of noise on smaller and smaller sensor sizes. The amount of noise one would expect from a small 24mp form factor sensor would be at least an order of magnitude higher than what one would expect from a 24mp FF sensor, despite the fact that both sensors can frame the same subject the same way, and produce images of identical composition.
Comparing cameras is more than just about resolution, though. A sensor not only has to resolve fine elements of detail, it also has to accurately reproduce color, produce images with low noise, capture a wide range of distinct, finely delineated tones (dynamic range), etc. Measuring all of these factors requires not only the necessary equipment and software, but also a certain amount of know-how and expertise. One must understand the theoretical fundamentals of digital imaging, resolving power, convolution, etc. to make an accurate assessment of any test data gathered.
If you are serious about getting into your own camera and lens measurement and comparison, then you should look into Imatest. Imatest provides the test charts and software you would need to do accurate lab testing yourself. Note that purchasing an imatest package is by no means cheap...it can cost thousands, if not tens of thousands, of dollars to build a proper camera testing lab.
Finally, comparing "compact to DSLR on even grounds" is an impractical goal to start with. That would be, quite literally, like comparing "apples to oranges". You can't really compare an apple to an orange on even grounds, outside of the simple fact that they are both "fruit". Beyond that fact, the two are entirely different, service different needs, and solve key problems in different ways, and are otherwise not worth comparing.
Fundamentally, anything a compact camera (and here, I take that to mean point and shoot, bridge cameras, anything else with a built in lens) can do, a DSLR can do better. These days, I would say any Mirrorless Interchangeable Lens Camera (MILC) can do better than a compact as well. Think of the three as layers in a tiered structure.
- Compacts cover the bottom tier...numerous, infinite variety, simple, easy to use, but limited in capability.
- Mirrorless cover the second tier, far more capable, more flexible, yet still relatively easy to use, offering superior IQ in a lot of situations. A multitude of interchangeable lenses for ILC designs offer an exponentially greater range of optical options and quality.
- DSLRs cover the third tier, larger, heavier than compacts or mirrorless, more complex and thus requiring a steeper learning curve, however vastly superior in terms of IQ, functionality, capabilities, lens options, and flexibility.
- One could even throw on a fourth tier, MFD (medium format digital) covering part of the range of capabilities that DSLRs cover (but not all of it), offering even more vastly superior IQ, a potentially steeper learning curve, but with more limited capabilities than DSLRs in some respects (i.e. high ISO, high speed shutters, highly advanced and extremely fast AF systems.)
Each tier can be compared on relatively even grounds with anything else in that tier. Some broad comparisons can be made between tiers, however one MUST understand that such comparisons are NOT on "even grounds", and the fundamental differences between cameras of different tiers thus implicitly make meaningful low-level comparisons difficult.
