Let's put some numbers to this:http://www.xbitlabs.com/articles/cpu...g840-g620.html
From what I glean from this article (Skip to page 8 fore G620 vs 2100T), a Pentium G620 is so close in performance to an i3 2100T, there's no reason not to save the money. You will miss out on hyper-threading, but it's likely you won't harness the advantages on hyperthreading on the type of machine you're building where you're considering an i3 caliber processor.
If you're trying to run a dual-cable tuner, record two shows, and watch a Hi-Def movie decoding HD sound simultaneously, then you're going to want to have a processor cable of hyper-threading, and maybe even a dedicated sound card to ease the pain and relocate some of that heat to a different component. However, if you're running XBMC and just watching movies served up from your home server it's likely that the SLIGHTLY reduced IGP on the G620 (It's still sandy bridge) will serve your purposes.
I'm planning on a G620 based HTPC without a TV tuner, so I'll have to eat my words if it doesn't perform, but the numbers look good.