Your question is not easily answered, at least in my opinion, but I'll have a go at it.
Your impression that larger airplanes are less sensitive to xwinds than smaller airplanes is correct, very much so in my experience. I lack the expertise to give you the aerodynamic basis, the equations if you will, but I'm fairly certain that saying an aircraft's sensitivity to a xwind is inversely proportional to it's mass, landing speed, and wing loading is a correct statement. As I remember, the max demonstrated xwind for a Cessna 172 is 15 kts, for a 747 either 25 or 30 kts, and I would much rather be landing a 747 in a 30 kt xwind than a 172 in a 15 kt xwind. In 747 sims we would occasionally crank the xwind up to 40 kts for an interesting but still safe landing.
Using extra speed in a small aircraft to help is not, in my opinion, a good idea. You'd certainly want to add a bit to your approach speed to handle gusting conditions (which typically accompany crosswinds), but what you need to do is transition from flying speed to non-flying speed as quickly as possible rather than extending the time of that transition. You need to get the weight off the wings and on to the wheels as quickly as possible.
There is one exception to what I just said. Back in the 1950s when I first learned to fly, they used to teach what they called 'wheel landings' for handling crosswinds in taildraggers. The problem with a taildragger is that the c.g. is behind the main gear. If you touch down in any kind of a crab, it wants to switch ends. In other words, a ground-loop. The idea of a 'wheel landing' was to get the main wheels on the runway with extra speed (after having slipped to the touchdown) so that the rudder (with the tail still off the ground) had plenty of authority to counteract weathervaning, and of course with the upwind aileron fully up. Then you were supposed to keep the airplane straight while the your speed dissipated to where the tail could no longer fly. I have no idea if they still teach that technique.
So now you're the PIC and having to decide whether to land in a xwind. Following are some of the things I can think of that might enter into your decision making:
What's your personal confidence level? If you're nervous about the situation you're probably not going to do as good a job as if you were relaxed.
What's your experience level in the airplane? Aircraft, even of the same weight class, vary in their handling qualities in a xwind, and the more you've flown them in xwinds, the better you're going to be in that model of aircraft in a xwind.
High wing or low wing? The closer to the ground you get the more the wind decreases, and that few feet of difference can make a difference. Also, I suspect, but do not know, that having most of the wing below the c.g. rather than above the c.g. helps.
What is the runway surface, and what is its condition? In other words, how slippery is it going to be. A dry paved runway is, of course, the best. However, a dry paved runway with a lot of reverted rubber in 120 F (49 C) temperatures can be interesting. Ice or wet grass is perhaps the worst. I put a Cessna 150 off the runway in wet grass back in the 1970s.
How bad do you need to land there? Some might say that doubts about being able to safely land should always override the need to land, but that's not the real world.
For a light aircraft, you may be able to turn that strong xwind into a strong headwind by using a taxiway. I've done that at a uncontrolled field.
A word of caution: Just because the xwind is within the max demonstrated xwind component does not necessarily mean you can safely land, it just means an experienced test pilot did it on a reasonable runway surface. The max demonstrated xwind is a guideline that is sometimes safe to exceed, sometimes not, and sometimes not safe to even get close to.
