Well bits is bits is a 'bit' of an oversimplification (sorry for the pun). There are 2 parts to digital serial streams, the data value (1 or 0) and timing. As others have mentioned jitter (timing) is the primary culprit in the CD digital world for bad sound. In reality as long as the digital data is there at the right time, then things are mostly equal.
Now having said that I believe it pays to get a good player mostly for the transport. I realize most laser pickups are made by 2 or 3 companies, but the software which does the tracking, motor control, drawer control, etc, is all different. I have ruined a few CD's on bad transports that caused the CD to shake and ended up scratching the CD.
Also important is the ability to do error correct which compensates for unreadable portions of the CD, stability of the clocks, etc.
I am oversimplyfying this a lot as there is much more that goes into getting the digital signal out of the CD.
Yes bits are bits but only when it comes to amplitude. Everything else can (and does)unfortunately vary.
My 2 cents worth is it pays to by good quality, but not go overboard.
Which is why be buy Outlaw products isn't it?