In general, compact binoculars will not offer the resolution (ability to distinguish very fine detail) as their larger siblings, simply because smaller binocular objectives (front lenses) cannot offer the resolution or performance of larger objective lenses. This is simply a law of optics regarding lens size and the ability to separate fine detail. In other words, a compact binocular will not appear quite as sharp and crisp as its equivalent in a larger binocular. Keep in mind, however, that we are talking in terms of all else being equal, comparing a compact binocular with the same brand and model in a larger version. When we begin to compare different models and sizes at different prices, we also have to account for lens quality. Lens quality can be just as important as lens size when it comes to performance. In fact, a premium (and expensive) compact binocular with high grade, perfectly ground and polished lenses can easily outperform a cheap full size binocular. We have to compare apples to apples, here.
A more significant shortcoming of compact binoculars, no matter what the quality, is eye fatigue, especially over long observing sessions. Smaller objective lenses on compact binoculars produce smaller exit pupils - the beam of light that exits the eyepiece and enters your eye. As a result, you must be more precise when centering the eyepieces over your eyes. On some compacts, even some premium compacts, being off just a little when centering the binocular over your eyes will produce detectable eye strain. For this same reason, it is also very important on a compact binocular to set the interpupillary adjustment (the width between the barrels to fit your eyes), very carefully. Opening the binocular too wide or not wide enough produces the same problem of your eyes not being centered, correctly, over the eyepieces and eye strain will result. Experience using a binocular will go a long way to minimize this problem, but I still use and recommend a full size binocular when it comes time to use a binocular for many hours a day. Compact binoculars are just not suited for long, hard observing sessions. Compact binoculars are at their best for more casual work.
One of the most common criticisms of compact binoculars is lower image brightness, for the same reason as lower resolution - smaller front lenses. While it is true that smaller lenses do not take in as much light as larger front lenses, this image brightness issue is very much over emphasized with compact binoculars. It gets repeated so often perhaps because image brightness is the easiest binocular concept to visualize and explain. However, it is a mistake to automatically dismiss a compact binocular as not being bright. In my actual experience, out in the field, in side by side tests with larger binoculars, a premium compact binocular can hold its own with a larger binocular in terms of brightness until it is nearly dark enough to need the lights of your car. That's enough image brightness for nearly any daytime use. Unless you really need a binocular for very low light conditions, it is a mistake to overlook a compact binocular on the basis of image brightness.
Small size and lightweight are the main reasons for buying a compact binocular, but these same things work against you when trying to hold a binocular steady. In full size binoculars, I generally recommend a magnification (first binocular number) of no more than 10 for the sake of image steadiness. A compact binocular in 10x is even harder to steady and use than full size 10x binocular because of its lighter weight. I still own and use 10x compact binoculars and prefer a 10x in a compact binocular for some applications, but image steadiness can be a problem for me with my 10x compacts. I often resort to bracing my 10x compacts against a tree or other impromptu support to get the steadiness I need. That's why I also own and use 8x compact binoculars. An 8x compact binocular is noticeably easier to steady than a 10x and the wider field of view of an 8x also makes it easier to get that elusive bird in the binocular field of view. My recommendation, therefore, is an 8x in a compact binocular for all around use, especially if this is your first compact binocular or you are new to binoculars, altogether.
Yes, less is more when it comes to magnification on the best compact binocular. Many beginners are lured into going more than 10x on a compact binocular, but that is nearly always a mistake. I do not recommend more than 10x (first binocular number) in a compact or even a full-size binocular unless you plan to use the binocular on a tripod, but be advised that very few compact binoculars are tripod adaptable. Besides, what's the point of carrying a compact binocular if you have to carry a tripod to use it, effectively? For the same reason (and a great many more, besides), stay away from zoom compact binoculars, altogether. Compact zoom binoculars are all but unusable at higher magnifications and, like all zoom binoculars, prone to some severe optical and mechanical problems. I never recommend any zoom binocular for any serious use.