We report on the results of a comparative investigation of highly dense bulk MgB$_2$ samples prepared by three methods: (i) hot deformation; (ii) high pressure sintering; and (iii) mechanical alloying of Mg and B powders with subsequent hot compaction. All types of samples were studied by ac-susceptibility, dc-magnetization and resistivity measurements in magnetic fields up to $mu_0H=160$ kOe. A small but distinct anisotropy of the upper critical field $H_{c2}^{a,b}/H_{c2}^{c}sim1.2$ connected with some texture of MgB$_2$ grains was found for the hot deformed samples. The samples prepared by high pressure sintering as well as by mechanical alloying show improved superconducting properties, including high upper critical fields $H_{c2}$ ($mu_0H_{c2}(0)sim23$ T), irreversibility fields $H_{irr}$ which are strongly shifted towards higher values $H_{irr}(T)sim0.8H_{c2}(T)$ and high critical current $J_c$ ($J_c=10^5$ A/cm$^2$ at 20 K and 1 T).
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