I was one of the like 5 360 owners that didn't download the first Geo Wars.  Is there any reason for me to download the first one (other than the cheaper price tag), or should I just go ahead and download the second one?  In other words, is there anything that the first one offers (other than achievements) that the second does not?

I loved the first game, but honestly, the second game is fantastic and renders the first one obsolete.  I freely recommend buying the second game, it's worth the money.

no, not at all.  The playing of the games is slightly different, where geo wars 2 puts emphasis on collecting 'geoms', which are score multiplyers.  Other than that, no.  The first Geometry Wars was basically just the mode evolved, whereas geometry wars 2 has evolved, deadling, pacification, kings, waves, and sequence.  Even the music from the first game is carried over in a remix into Geo Wars 2. 

So short answe;, there's absolutely no reason to buy or play the first geometry wars now that 2 has been released, and i've actually deleted the first off my hard drive.