There are way too many variables to both hand cutting and grinding to make some a simplistic comparison.
For hand filing, You have to be able to consistently maintain file depth in the cutter (hook), cutter angle same on all teeth, cutter angle 'straight' on each indivdual tooth (not waving around), cutter length, and file 'drop'. Then keep all these the same on both left and right cutters, regardless of one cutter perhaps being harder than the others. Just doing the same number of strokes on each tooth isnt going to cut it. As a beginner you need to start with file guides to take a couple of the variables out, and use verniers. As you get better, you can hand file and get pretty close just by eye.
For grinding, A lot of cheaper grinders just arent that consistent. They vary from left to right, and flex. Add to this the different types of wheels available, dressing the profile of the wheel getting the settings right, not burning the cutters. Using a good quality CBN/ABN wheel on a top quality grinder is completely different from using a poorly dressed pink wheel on a $30 ebay special.
It's pretty tough to pick between a top quality grinding wheel/grinder in the hands of a pro sharpener vs a top quality hand sharpen by someone equally skilled. Having said that, it takes regular practice to get good at hand sharpening, and i you aren't using a saw that much you may not ever get good at it. I've met plenty of full time saw users that are absolutely awful hand sharpeners.
If you are not a good hand sharpener, a cheap grinder/wheel isn't going to improve your situation at all. A top quality grinder/wheel will be far superior to a low quality hand sharpen, and 90% of people will get sharper more consistent chains with less effort this way. Over the life of the grinder/wheel, you probably have come out ahead compared to buying files too. Adding to that, careful use of a grinder will get more sharpenings out of a chain than hand filing will in my opinion. Some users are getting a couple thousand chains out of these combos, if you're paying a buck a file and only getting a few sharpens average out of each file by the time you factor in files you lose, files that rust, files you break, files you destroy on overly hard cutters etc....
But you still need to know how to hand file so you can touch up.
Shaun