I think I can close grip press roughly the same as I can incline press, maybe about fifteen pounds more on incline. My bench doesn't quite adjust high enough for a true incline press so this might account for the higher weights on incline.
I think it's easier to get a good drive with the legs on close grip presses, so if you are proficient at using your upper traps/shoulders as a solid base to drive off of and are good at driving your feet into the ground (and your hips/lower back) upwards, you can create more maximal force output on close grip presses.
It depends on the bench, but generally I find it harder to do all of this on incline press benches as opposed to flat benches, regardless of hand position.
Of course, some people (like myself) don't have really broad shoulders or naturally strong upper backs and shoulders. I've always had pretty good strength in my arms from working construction and my lower back is really strong, but I've had shoulder impingement issues from years of pitching that probably account for a discrepancy between the two presses.
The bottom line is that the two lifts, if done with the same volume and intensity over a long period of time, are probably not going to be equal due to any number of outside circumstances that may have nothing to do with your training methods.
As for being weak at the bottom of the press, you'll always be weakest there. At the bottom of any weightlifting move (or at full extension on curling-type moves) your muscles are stretched out and the fibers are unable to "grab" each other to create more force output. As the muscle becomes less stretched out, the move becomes easier.
You could probably do 5-10 partial reps at the very top of your bench by bringing the bar up and down just a few inches with 10-25% more weight than your one rep max. This is a great way to stimulate your central nervous system.
So you'll always be weakest at the bottom and there is simply no way to improve upon this weakness without also increasing your strength at the top. The two ends of the movement will always have this discrepancy.
You can get better at creating more force output at the bottom by strengthening your abs to help drive up through your hips and torso on squat-type movements and by improving your form on presses, but that's about it.