I have the Daystate 120v compressor, and yes you can fill the gun directly with it. However, it would take more time setting up this particular compress to fill a gun, than a tank. The smaller compressors are better suited for filling guns, than big tanks, however.
All that said, there is a significant convenience to having a tank for they can be toted in the field easier than a compressor.
Note: I started out filling with a hand pump for a few years, and then went to a SCUBA tank, which I still use for some things. The local dive shop gives me free refills and visual inspections since I purchased the tank through them. This is clean dry breathing air which is what I'll keep in the SCUBA tank. Once I got a PCP that had a regulator, the desire to fill to higher pressure became a bit of a problem. I started the fills with the tank, and then topped off with the hand pump. For casual use, this worked quite well. Once I started shooting over 100 shots per visit at the range during local competitions and in practice, I decided that an SCBA high pressure tank (Tiger Shark from Joe Brancato) and compressor were worth the expense.
My choice in the tank and compressor were due to sponsorship support for particular competitions, though more expensive than other options.
ETA: Dryers are more critical during humid days or climates. If I fill on a cold winter day here, there is no water collected in the separator that is built into my compressor. I do, however, on most days that I fill, pre-dry the air by passing the intake through a filter I made that contains desiccant.