Depending on how far from an outlet you are, and how much air you need, I think you'll be very surprised at how versatile even the smallest shop air compressor will be. Thin extension cords can prevent the motor on some higher powered compressors from starting, but if you get a small 1/3hp to 1hp sized compressor, the issue should be minimized.
Another benefit is that you can plug in the compressor, let the tank fill up, then unplug it and take it to where you need to do your work. Depending on how much air you need, it might make it portable enough.
I think that most 12V inflators are really only good for occasional tire filling, very short duty cycles. Even the least expensive and smallest compressors should work better for your needs.
As your first real compressor, and knowing that you've gotten by with a tire inflator in the past, I would suggest getting an inexpensive bundle air compressor. Something around the 1hp range or less, with a tank in the 1-3 gallon size that includes the basic coiled hose and some fittings. Should be around $100.
Like this:
http://www.homedepot.com/p/Husky-3-gal-P...13HPD/202868804
http://www.lowes.com/pd_375114-1126-FP2048___?productId=3533376&Ns=p_product_price|0&pl=1&Ntt=air+compressor
What do you usually use the inflator for?
btw, I am no expert on compressors, I just got my first one a few years ago, it is just a small 3 gallon compressor, but with it, I can air up tires much more easily, and have since picked up a 23ga pin nailer and brad nailer for some trim work at home.