It really depends on which Pentium Dual-Core you are talking about and which Core 2 Duo. If the Pentium is a 65nm one (the desktop Pentiums are all 45nm now, not sure about the laptop Pentiums), and if the C2D is a 45nm one, then the C2D will use less power.
If the Pentium is 45nm and the C2D is 45nm, then it'll use the same. If both are 65nm, then it'll use the same. Back in the old days, Intel would cripple the power-saving features on the low-end processors, but they no longer do that, and the Pentiums have the same power-saving features like EIST, C1E, etc.
(Modern) Pentiums are the same as C2D except for different branding, a reduced cache (but NGMA isn't nearly as cache-dependent as Netburst, so this is not a big deal), and no VT (but the low-end C2Ds also lack VT). In fact, they use the exact same cores, and the differentiation between Pentiums and C2Ds happen after the wafer is made, during the final phase of production.
In terms of energy use, there is no difference (assuming that the Pentium and C2D both use 45nm or both use 65nm). In terms of performance, the reduced cache will slightly reduce the Pentium's performance, but not significantly. In terms of value for the cost, the Pentium is the clear winner. The posts saying that the C2D is clearly better than the Pentium are bunk.
Update: zigzag3143's implication that Pentium Dual Core does not support 64-bit is flat-out incorrect. All non-Atom Intel chips since late 2006 have supported 64-bit, whether it's a lowly Celeron or a high-end i7.
PS: Intel retired the Pentium brand some time ago, but then revived it as basically a rebranded Core 2 Duo with a reduced cache. Perhaps the other posters in this thread were thinking about the old Netburst Pentiums, which have been out of production for years.