They will both work fine indoors. The "better" part could come into play if you need to use something other than omnidirectional antennas, or if you plan on using PoE.
The 1142 has fixed (non-changeable) antennas. The 1250 has RP-TNC antenna connectors that allow you to use any approved antenna.
The 1250 sucks a lot more power than the 1142. "Normal" 802.3af-compliant PoE gear will not be able to power a 1250 with both radios running at full xmit power.
Also - I remember hearing about the 1142 providing better benefits to legacy (802.11a/b/g) clients than the 1250. Something about the "M-Drive" (MIMO), but I can't find anything conclusive. Maybe someone else can jump in with more on that.
I will be using the power injector to power the 1250. My deployment is on a house next to the beach; so I just want to learn if the 1252 will give me more coverage since it allows me to use different antennas
"More coverage" is difficult to define, especially since the radios put out the same signal strength (I'm pretty sure). But you can definitely use different antennas to provide "different" or "better suited" coverage with the 1250. For instance, let's say your house faces the street and backs up to the ocean, and that you don't want to provide wireless coverage to the street in front of your house, but you do want to provide coverage in house and in the back beach area. A patch antenna mounted on the front wall of the house aimed towards (facing) the rear/beach could accomplish that. You would not be able to do that with an 1140.