As far as games, updates and custom firmwares go, there is nothing the slim and lite has that the phat won't have too. They're essentially the same, except the slim is lighter, consumes less battery power, and has a twice the predictive cache size to reduce loading times in UMD based games (if you use downloaded/pirated games, which we are not allowed to direct to, then you will not notice any difference. Also any new firmware as of 2.6x will be compatible on both, and will always be compatible on both. You just can't get a slim and lite down below 2.6x.
This is because the phat has 1 advantage that the slim and lite cannot have - 1.5 kernal. This kernal is used in many of the older homebrew and some of the new homebrew, as well as many of the downgraders, meaning that they will NOT run on a slim and lite. There are various solutions to this, such as eLoader, but more commonly homebrewers are recompiling their homebrew or just writing new homebrew specifically to be slim compatible, using 2.6 kernal or above.
Popular opinion also goes that if you try a PSP slim, you will not want to go back to the phat, just because of the extra weight and bulkiness of the phat. I have both, but I only use my slim.