With 1H NMR a useful spectrum can be obtained very quickly (5 minutes) with a few milligrams of material, however with 13C NMR normally the minimum scan time would be longer (~20-30 minutes) and a more concentrated sample would be needed (~30 mg/0.6 mL) to obtain a useful spectrum. The amount of material needed should be increased as the molecular weight of the compound increases, I think I was previously told ~5 mg of sample per carbon atom per 0.6 mL of solution. So if you have an compound with a single aromatic ring 30 mg of sample may be fine but for a larger molecule 100 mg may be needed. If you only have 30 mg of a larger molecule then 4-12 hours of scanning time may be required.
In 1H NMR more information can be obtained: integration, multiplicity, coupling. However by running DEPT type 13C NMR experiments different carbon environments can be identified. Look for APT (attached proton test) (C, CH2 in one direction and CH, CH3 in the other direction) or PENDANT (CH2 in one direction and CH, CH3 in the other direction) pulse sequences.
2D NMR experiments such as HSQC and HMBC can be important for fully characterising more complex or new compounds. They bring together both 1H and 13C NMR and show correlations between proton and carbon atoms. HSQC shows the carbon atom which is attached to a proton atom (single bond C-H) and HMBC shows multiple bond interactions between carbon atoms and protons (eg. C-C-H).
A few additional comments: In problem solving, a good general rule is to start with the simplest, fastest, most cost-effective tool. In solution NMR of organic compounds, this is 1H NMR, followed by 13C NMR which normally takes longer and may require a more concentrated solution. If one-dimensional NMR techniques do not give you adequate information, then employ 2D methods. If there are additional atoms (e.g., N, S, etc.) in your molecule, multinuclear magnetic resonance will yield further information. I your compound contains fluorine, 19F NMR is also a useful technique. For very small samples or very dilute solutions, cryoprobes may help. All this assumes that the required equipment is available to you. You may want to check out 1D and 2D NMR Experimental Methods - Emory University and/or Structural Elucidation of Small Organic Molecules by 1D, 2D and Multi-Dimensional Solution NMR Spectroscopy on the Internet for a lot more detailed information. If you would like to see an example of complete characterization of a small organic molecule by 1H, 19F, 13C, 15N, and 17O NMR, check out Multinuclear magnetic resonance analysis of 2-(trifluoromethyl)-2-oxazoline (Magn. Reson. Chem. 2005; 43: 867-868). (If you have no access to this publication, I'll be glad to send you a reprint by post.)
1H NMR is used to determine the type as well as the number of hydrogens in a molecule. 13C NMR is used to obtain information about the carbon backbone of the compound chemical structure.