That comes with practice. The difference is with a linear cursor, I can move to any area of the screen or face any way in a game and know the distance with muscle memory. With an accelerated cursor, you have to judge the speed at which you move there, which is nearly impossible to predict. As such, whereas you can "snap" to a position with a linear cursor, you need to slow down as you approach it with acceleration.
Here's are some good tests, although they might not work that well if you're not used to linearity. Find a shooter (TF2 works well). Now point at something, then move the mouse slowly to something else. Now dart back to the first thing. You need to move the mouse a different distance. Try moving the mouse the same distance at the higher speed and you'll fly off past it. A linear mouse would end up exactly where it started.
Now, open up paint. With acceleration off, try drawing a continuous circle (pencil, 1px), speeding up as you go. 90% of the time, it will start skewing and look more like an orbit. Do the same with a linear mouse and you can get much more accurate circles.
Sure, if you're trying to hit a particular pixel in photoshop, then the cursor slowing down can help compensate for lack of natural precision, but you also have a lot more time to get there. You don't have to leave the sensitivity high, though. A linear cursor with a low sensitivity is super accurate. I use ~1000DPI with Windows at the default {which you don't really want to change for reasons I won't go into.} I doubt you'll find ANY professional/elite gamer that plays with acceleration
With regards to gaming vs normal mice, you have two main differences: resolution and response time. Whereas normal mice have a locked resolution (usually 400, although many are using 800 and even 2000, now), gaming mice allow you to set it (many can change on-the-fly) to whatever you want. Having a higher resolution (measured in DPI or Dots Per Inch; or Counts per Inch for Steelseries) gives a more precise reading of the movement your mouse makes. It also allows you to adjust the true sensitivity of the mouse without Windows' sensitivity slider (where anything than the default middle setting screws with the tracking BADLY). Just as important is the response time. Whereas standard mice poll (check the change in position relative to the last check) every 8ms/125Hz, gaming mice poll at 1ms/1000Hz. Normal mice can feel lethargic in comparison. Now some people will say that people can't notice the difference or that screens only refresh at 60Hz. The thing is that it all stacks up. Firstly, just because the screen only changes every 1/60th of a second, that doesn't mean the game doesn't (which is why a lot of elite gamers play with 120Hz monitors). Your movements between those frame updates are still tracked and they still matter. Secondly, when there's x time from the mouse, y time from the game, z time to the GPU and t time to the screen, every little millisecond on the mouse is amplified.
Would go on, but I need to pick the dog up from the Vet and that's pretty rambly already. :P