'Bob B' does give good advice. But, I'd like to add my $.02 as to why I think the cabinets should be installed first.
First off, I hope your cabinets / countertops are high enough to slide in your dishwasher and stove. There isn't anything worst than finding out you can't get your dishwasher under the countertop! Now, depending on the clearance you have with that and the stove, first take a look at installing the cabinets first. IF you can get the dishwasher OVER the backerboard+tile, and UNDER the countertop, then I'd install the cabinets first. IF you can't then you'll have to raise the cabinets UP (either w/shims or a tiled floor) to get them under there.
IF you decide to do the whole floor in tile BEFORE you install the cabinets, what if down the road you want to install vinyl? You'll have to remove the tile and backerboard and lay down an underlayment to that's 'thick' enough to bring you back to bottom of the cabinets. You see, by installing the tile first, you'll have to 'adjust' a new floor to that height. This may mean you'll need a molding at the base of the cabinets. Granted, if you shim, you'll need molding anyways, but you'll need to look at what it will look like too.
I'm too much of a planner so that's why my mind is wandering down the road. Objectively, from a cost perspective and (in a way) from a practical perspective, especially when it comes to ceramic tile, the cabinets are installed first. If you're talking about sheet vinyl, one might consider laying the entire floor first (before installing cabinets) because if you did the cabinets first, the 'cut sheet vinyl' would be thrown aways anyway.
BobB's point about being able to get the fridge out too is a good one. If you want to 'test' out your dishwasher situation, just get a sheet of backerboard or plywood that would be the COMPLETE thickness of your backerboard and tile, and see if you can slip it under the countertop on your cabinets.