Okay, so the thread has apparently morphed from the question of whether karate has better kicks than hands to the entirely different question of boxing hands are better than karate hands. Let's do some analysis on this new question ...
First, there's the question of "better for what?" The systems in question were developed in different contexts for different purposes.
Boxing was developed as a form of one-on-one sport competition, with rules that have evolved substantially over the years. It has also been promoted for pretty much the entire span of its existence as a legitimate tool for self-defense purposes. Its techniques and training methods have also been absorbed into a number of eclectic martial arts designed for street self-defense/combative purposes.
Karate was developed as a form of unarmed civilian self-defense and has evolved in a number of directions - light contact (tag) competition, full-contact competition, artistic performance competition, self-discipline, self-defense, and so on.
It makes no sense to expect that a karateka could dominate in a boxing contest or that a boxer would do well in a point-sparring or forms competition, so let's find a neutral ground. Let's look at a one-on-one, unarmed, bare-knuckle street fight and examine how boxing and karate training methodologies will affect the effectiveness of their hands in such an environment.
The first thing I should note is that it's tricky isolating just the "hands" part of the equation. What makes a boxer's hands effective are not just his punches, but his footwork, head movement, conditioning, and other factors as well. To do this comparison properly, we're going to have to take more of an holistic view of both arts. Let's go step by step ...
Hitting air: shadowboxing vs kata. Shadowboxing is a free-form exercise sparring against an imaginary opponent. In order to have much benefit beyond a simple warm-up, the fighter needs the experience and mental focus to visualize and respond realistically to the imaginary foe. In contrast, kata are pre-arranged patterns that , according to their proponents, contain the essential lessons of the system. There is considerable disagreement among karateka regarding the meanings of the movements. Are the stances exaggerated for the sake of exercise or not? Does a given movement represent a strike, a block, or a throw? Is the kata just teaching principles of movement or does it represent a specific sequence of moves in an actual fight? Is the approach to performing kata that scores well in competition useful in developing actual fighting skills? The answers will vary considerably from instructor to instructor and some practitioners will tell you that most other practitioners are doing it wrong. Given all this, I am going to say that the effectiveness of kata in preparing for a fight will depend on the individual having the knowledge, experience, and focus to visualize realistic application while performing the kata.
Verdict: Draw. It depends on the individual.
Hitting stationary targets: Boxers make serious use of the heavy bag to develop power. Karateka traditionally used the makiwara, although some now use the heavy bag instead. So far, so good, but many modern karate schools have let this aspect of training slide and spend most of their time punching air instead.
Verdict: Draw, if the karateka trains at a dojo which spends substantial time on the heavy bag or makiwara. Boxing wins, if the karateka spends most of his time hitting air, as many do.
Hitting pads: Boxing has developed pad holding into a sophisticated art where the pad holder acts both as a trainer and a sparring partner - feeding openings, forcing movement, and exposing weaknesses. In contrast, every time I've seen a karate instructor holding pads, it's been more of a static thing which is much less useful.
Verdict: Boxing wins. Caveat - there's nothing stopping a karate instructor from learning how to hold pads like a boxing coach. I can't see anything that would violate the principles of karate in doing so.
Sparring: Continuous sparring with (substantial) contact is standard at any real boxing gym. Unfortunately, a very high percentage of karate schools spar either non-continuously or with limited contact or both. Of those that do spar continuously with hard contact (like Kyokushin Ryu), some don't allow punches to the head, which can lead to bad habits.
Verdict: Boxing wins in most cases. However, there are karateka out there who do continuous sparring with hard contact, including head punches. For those practitioners, the result is a draw.
Hand conditioning: Modern boxers mostly train with boxing gloves, which not only protect the hand but force the hand into an incorrect position for bare-knuckle punching. The old methods for bare-knuckle boxing have been largely forgotten by most practitioners. In contrast, many karateka still work on conditioning the hand for striking hard surfaces (such as a persons skull) with the bare hand.
Verdict: Karate wins.
Footwork: Boxing develops excellent footwork for controlling distance and angles. Some karate schools have let footwork deteriorate into a game of bouncing back and forth playing tag along a straight line. However there are still plenty of karateka out there who know how to use excellent angular footwork.
Verdict: Draw
Head movement: Boxers have developed advanced methods for evasive head movement which make it very hard to land a punch to their heads. I have never seen anything equivalent in any style of karate.
Verdict: Boxing wins.
Targeting: Boxers train to mostly limit their punches to legal target areas. (Some are perfectly willing to hit to the groin or the back of the neck - but only when the ref can't see.) Some karateka operate under a similar range of limited targets, but others do spend extensive practice targeting vulnerable spots such as the groin, throat, eyes, and back of the neck. It's not that hard to adjust to new targets in a new context, but the person who is used to targeting those points should have an edge.
Verdict: Karate wins.
Physical conditioning: Conditioning to build strength, endurance, and physical toughness is an essential element of boxing training. It's traditionally an essential element of karate training as well, but one that has been watered down in a large percentage of dojos. This has a lot to do with the target audience of students. Boxing gyms are typically aimed at building competitive fighters. Many karate dojos are aimed at providing a fun hobby for the whole family and aren't going to push so hard on the conditioning aspect. However, there are still karateka out there who train conditioning hardcore.
Verdict: Boxing wins for the "average" boxer vs karateka. Draw if both fighters are serious athletes.
Kicking: Wait, what? I though we were just looking at hands? Correct, but we have to take an holistic look at the use of those hands in context. In good karate, the legs should work to set up the hands (and vice-versa). It's a lot easier to land a punch when you've just kicked your opponent in the groin or swept his leg.
Verdict: Karate wins.
Grappling: (See my comment above regarding kicks.) Modern boxing no longer includes throws, but professional boxers can be suprisingly sophisticated in their use of the clinch to stifle punches, tire out the opponent, set up their own punches, and even apply subtle dirty tricks such as arm wrenches where the ref can't see. I know it just looks like they're hugging each other, but there's more going on than that. Karate (depending on the style) can include a variety of grappling techniques, such as throws, sweeps, hand trapping, and arm bars. However, most karateka don't spend a lot of time sparring with these grappling moves or developing them to a high level of sophistication.
Verdict: Draw.
The actual hand strikes: jab, cross, hook, uppercut vs jab, backfist, reverse punch, knife hand, etc. I put this last because I consider the details of the techniques to be less important than the training methods. Karate has more officially named hand techniques, but boxing has enough variations on the basic punches so that an individual fighter probably has about the same number of go-to moves in a fight. The boxer will probably be more polished with his punches, since he doesn't have to dedicate training time to kicks. As far as the merits of the actual techniques ... I'm partial to boxing, but I totally respect the punching technique of those karateka who actually train and fight full contact. As I noted in another thread, in the heat of an actual fight a reverse punch and a rear cross start to look awfully alike.
Verdict: Boxing has an edge due to specialization and practice.
Overall verdict: A typical competitive boxer will have a strong advantage with hands over a hobbyist karateka (even a black belt) at an average dojo. If the karateka is a serious fighter from a hardcore dojo that trains full contact, then the fight is much more even.