A lot of it is how old and “established” you want your characters to feel.
3 LPs is actually pretty strong. You can build Squires, Augurs, Rogue Wizards, Doctors, Striders, cagey Criminals, et cetera. Characters will tend to be around 16-23 and reasonably well-trained, with just enough room to cover a broad base or really specialize in some focus area. But you’ll probably start out feeling like you’re missing something – a few more skill points, a stat you wish was just a bit higher, some reputation or trait you really wanted. That’s fine. It’s good. It gives you a nice clear thing to work towards, right away. (“I’m poor and I really need X right away” is a great basis for a first-session Belief, in my experience.)
You can expect to fail a good bit, but you’ll end up raising a lot of skills quickly, and, often, baked into your character is the sense that you can afford to fail a little – narratively speaking, I think we’re very used to seeing a squire trying to earn a knighthood, or a journeyman mage with new power, a brazen teenage criminal, &c. screw up, take their licks, and keep on marching; so the setbacks that can accrue just make their relatively rapid development seem fitting.
4 LPs, if you’re picking the powerful and goal-directed ones, makes you a solid, serious contender. You’re like 24-32. You might have been practicing your craft or rising up through the social ranks for a decade or more. If you take a lot of social/intellectual lifepaths, you can manage to have a B6 in a mental stat without totally tanking the other one. You have enough resource points that you can afford a home, a business, your own street gang, some serious military gear, or even some truly advanced spell knowledge. You should still feel a pinch in places – Burning Wheel doesn’t like to give you characters that already have everything they need, and IME you should generally avoid playing those characters when you do find ways to create them, because the motivation to turtle up is just so much higher – but you’ll start out with a lot you can throw at any situation.
If their lifepath skills already tie into the situation well (i.e. you’re not playing a middle-aged farmer who suddenly has to go hunting vampires), these characters are great for plunging into high-stakes stuff. Because they’re powerful and resilient, IME, you absolutely have to make sure they’re deeply motivated and facing worthy opposition from day zero. If you let them sit around to grow complacent I think there’s a risk of such characters becoming a overly cautious and fragile much faster than 3-LP protagonists would.