In the photoshop timeline panel, click on the icon in the upper righthand corner of that panel. When the menu pops up, select document settings. Here you can change the timing to what ever you want. The higher the frame rate the faster the animation will be. The frame rate is like saying how many frames do you want to pass in 1 second of time. Hence the higher the number the faster the animation.
The issue with good timing stems from placing the animation inside a web browser. This is most noticable when using a gif format. As this format relys on the browser for the timing and can therefore run extremely slow.
This issue will hapen no matter which app you create the gif file on. When creating large animations it is much better to use a format that can handle it, such as avi, mov, swf, flv and few others.
Any video that is using one the "better" formats can easily be ported into After Effects. The main hurdle is the codec, but it was created on your system, then odds are good it will load into After Effects. There are exeptions of course such as currupted files, formats like swf, which are really meant as an end of the process format. (meaning use that format for sharing rather than editing) If it is for flash use flv instead, it is much easier to import into other editing apps.
Which format you choose to use will depend on your audience, the size of the file, the quality of the file, what media it will be played on. Take into account the operating system if it will be played on a computer.
Hopefully this helps.
BTW, if you plan on creating from scratch, make sure you save the file in the native file format, so you can go back and work on it again. Also psd and ai file can be imported into after effects so keep that in mind if you decide to work on the file in AE.
How do I create a simple cartoon animation in Photoshop and transfer it into AE for better timing?
Don't bother creating any "animation" in PS, just the characters and other itmes. Separate all elements to layers for arms, eyes, mouth etc. and then move on to AE. Anything you do in PS beyond that will go to waste - AE doesn't see PS animation and such files usually cause import problems in AE. Likewise video layers may be troublesome and aren't supported in AE CS6, anyway....