A couple thngs to note.
Digital TV antenna is marketing mumbo jumbo. the antenna has no idea if the signals it receives are digital or analog.
NOw since the Dtv crossover a few years back, a large portion of TV stations went from broadcasting on VHF frequencies to UHF frequencies.
Antenna designs can be changed to better pick up different frequencies, and a digitally optimized tv antenna usually means it is just an antenna optimized for UHF reception. The higher the frequency, the smaller the antenna elements need to be.
Now a tube TV draws a lot more electricity than a new LCD backlit TV. Is this a factor?
Usually it is.
Getting a digital converter box to install on an old NTSC( analog) TV also requires power. There are some 12vDC converter boxes available, but most require 120Vac, and an inverter.
So this just upped the power requirement again. Is this a factor?
Usually it is.
One more factor is the use of the inverter to power a digital converter box. Inverters can be electrically noisy, causing interference to TV signals. My inverter can knock out some TV stations which come in at 100% signal strength when the inverter is off.
One more factor is the cost of the converter box. It could very well be 2/3 the price of a new flatscreen TV. So pursuing this route can certainly be penny wise and pound foolish, or kilogram foolish.
An AC/DC tv, one which does not require an inverter, is the best way to minimize battery consumption and minimize the possibility of interference and maximize the available channels one can receive in any given location.
Digital signals are all or nothing. if you have a ~30% signal strength, then the picture is just as clear is if you have a 100% signal strength.
If the signal gets weaker then Pixellation occurs, or the screen freezes and goes blank, where as on analog TV the screen just got fuzzier and fuzzier the weaker the tv signal got.
With Antennas, height is might. Omni directional antennas might be convienent and work well when close to broadcasting stations, but non omni directional antennas can get signals from 4 times the distance, when Aimed properly.
If you get a directional antenna, and aim it correctly, the chances you can get a workable signal are about 400% more than an omnidirectional antenna.
http://www.tvfool.com/index.php?option=com_wrapper&Itemid=29
Also note that with dtv, a station might come in as 7.1 on your TV, but could be broadcasting on channel 51.
In my area all the VHF high stations (7 to 13) are still operating, and I need VHF elements( rabbit ears) aimed at the towers to get those stations. Many of them are 92 miles at 5k' elevation away and I often get them at 100% signal strength, and some other days I get them not at all, due to atmospheric conditions. Dry Santa ana events wreak havoc with my TV signals. Foggy weather enhances them, sometimes to an incredible degree and I can pick up stations from Santa Barbara, about 200 miles away as a crow flies. TV signals over bodies of water propagate beautifully.