First, your terminology has created a "bit" of confusion in this thread, as you are discussing "Tips" not "bits" Bits are used to drill holes, tips are for driving fasteners.
Now on to a few issues that you are facing. First, an electric drill is about the worst thing to use to do the job. It has no ability to limit torque, so if you were not stripping tips, and chewing up the "Phillips head" screws you are using, you would probably be just snapping the heads off the screws. Screw guns look like electric drills, but they have a magnetic tip holder, not a chuck to hold the bit, and they have a clutch that spins free, once the fastener is inserted to a specific depth. Next, slotted screws are too shitty to even speak of here, and they should never be used, if you can avoid them. Phillips heads are marginally better, but as you found out, they still suck. Heading toward the "doesn't suck" end of the spectrum would be "Robertson head" or square drive screws, these have a small square recess that can be driven well, and are a big step up. Canadians seem to be pretty fond of these things, but us yanks are a bit too thick when it comes to upgrading to things that make sense, so we still suffer with slots and phillips, mostly. As mentioned on this thread, the Mac daddy, dog's balls, king of screwing is the Torxs screw. These have a star shaped recess, and once you try them, you will wonder if enlightenment is just around the corner, since your whole world just got a "bit" better. Good luck, and may you screw in peace.