Competing against a 10 Speed Bike with 7 Speed bike?
I'm not necessarily sure that the number of gears here is the key issue - it's going to be the upper and lower range: what are the extremes of your gear ratios (or gear inches, if you'd prefer)? 

Maybe your largest gear just isn't large enough. Maybe you need a bigger front cog (or a smaller rear one) to allow you to get up to the same ratio that he can use. 

cadence * gearing = speed


The extra gears on his bike just means the transition between gears is smoother - less of a leap between neighbouring cogs.