Particle width is one fairly global way to distinguish a Standard Model Higgs boson from similar beyond the Standard Model impostors without getting too far into the weeds of looking at every possible individual decay cross-section data comparison. Analysis of experimental data involving data including the estimated Higgs boson width, for example, has helped to rule out a simple fourth generation Standard Model variant.
The Standard Model Higgs boson, if it has a 125 GeV mass, would be predicted to have a 4.07 MeV width with an uncertainty of +/- 4%, which is derived from the sum of its cross-sections of particular kinds of decays. (The width of the Standard Model Higgs boson is a non-linear function of its mass).
By comparison, in the latest global fits made with the data announced this week, the width of the W boson is 2.091 +/- 0.001 GeV and the width of the Z boson is 2.4954 +/- 0.0014 GeV. The width of the top quark is 2.0 (+0.7-0.6) GeV. The width of the Standard Model Higgs boson is about 1/500th of these amounts. If the Standard Model Higgs boson had instead had a mass of 200 GeV its width would have been about 2 GeV.
Those arise from a combination of Standard Model Higgs boson branching fractions (bottom-bottom 58%, WW 21.6%, digluon 8.5%, tau-tau 6.4%, ZZ 2.7%, charm-charm 2.7%, and diphoton 0.22%), and production mechanism cross-sections (gluon fusion 15.3 +/- 2.6 pb, vector boson fusion 1.2 pb, W boson associated production 0.57 pb, and Z boson associated production 0.32 pb) (all per the linked article in the following sentence). The width is too small to measure directly at the LHC or any other existing collider.
A February 26, 2013 paper provided an analysis with slightly more up to date numbers and somewhat more involved analysis that placed an approximately 14% bound on exotic decays at the one sigma level, using the same methods.
I have not yet seen a published post-Moriond paper with an updated Higgs boson width estimate. This month's announcements from the Moriond Conference, and in particular the greatly reduced diphoton cross section relative to the Standard Model expectation at CMS which previously showed a large excess in this decay cross-section, have demonstrated cross sections closer to the Standard Model expectation. The new data has also refined the mass estimate upwards somewhat.
Taken together, this new data should reduce the estimated width of the Higgs boson from 6.1 MeV towards 4.1 MeV and narrow the error bars around this mean value.