Input bias current is the current that potentially comes out of your input pins, and its impact may be multiplied by your gain, depending on your configuration. Add a current source at each input corresponding to the bias current, and figure out if the resulting offset is important to you. Do this for the MAX values, and ignore the min.
Take your input noise density, and multiply by the gain and bandwidth to figure out what your output will look like.
It looks like the TLV272 wins for bias currents (maybe a factor of 3), and loses for noise (order of magnitude).
For temp measurement, you can reduce your bandwidth to get rid of the effects of noise, but dealing with offsets can be more troublesome
ADDITION:
Some of the discussion leads me to point out that when doing design like this, an engineer would generate an ERROR BUDGET and then figure out how to reach it. In this case, I'd probably start with quantization noise, and figure out if I need my output to be full scale-- i.e., do I need a rail-to-rail output in the first place? Then I'd factor in noise, nonlinearity over the scale of interest, and the effects of bias current. If bias current turns out to be a big consideration, but quantization noise doesn't, I'd be inclined to opt for a non rail-to-rail op amp, but with low bias and noise, and avoid the design tradeoffs needed for design of rail-to-rail amps.
It's tempting to design to the strategy that EVERYTHING should be built as accurately and precisely as possible, but its an incredible waste of resources. The best engineers figure out what the specifications need to be, and build to them. If you see an engineer or an engineering team that consistently EXCEEDS specs, then you're looking at a waste of resources.
The LT1630 lists a bias current up to 1000 nA (1 microamp). This is the amount of current coming into both input terminals. For a DC signal, the upper circuit will compensate for this error while the lower circuit could have an error contribution as high as 1 ua x 50 K (the signal impedance) or 50 mv.
The maximum input offset current is 150 nA, so you are contributing a worst-case 7.5 mV (150 nA x 50K ohms) of error by using a 50K feedback resistor.
Best Answer
"Rail-to-rail" is a marketing term used to describe an op amp whose dynamic range is able to reach the extremes of the supply voltage. This can refer to either the output or both the input and output.
It is not possible for the output to exceed the positive or negative supply voltage (which is why these are commonly referred to in US-English as "supply rails"). This is one of the key differences between the ideal op amp model and the real article.
As a counterexample, the ancient LM741 op amp is not "rail to rail", and here's why: in the datasheet Electrical Characteristics table, the Output Voltage Swing is rated +/-16V under the test condition of supply voltage=+/-20V. So the output can only get within about 4V of the supply rails. (There is some dependency on the output load resistance.) This is the key specification you can check on the Electrical Characteristics table pertinent to rail-to-rail output.
This limited dynamic range is very problematic at lower supply voltages. Attempting to operate the LM741 from +/-5V supplies, leaves only about +/-1V of dynamic range for the output. And operating LM741 from a single +5V supply leaves no dynamic range at all: the output is generally stuck in the middle and LM741 is not usable at such a low supply voltage.
It's also possible for some op-amps to accept inputs that are at or even beyond the rails -- Maxim Integrated makes a line of op amps marketed as "beyond the rails" (for input).