New chain, pedal power seems weaker
Your symptoms sound like your rear deraileur needs to be re-adjusted.  If that is off you will notice the skipping and "rattling" sound as the chain rubs against the deraileur or jumps gears under various pedal pressures.  That rubbing will also slow you down. 

Your old chain will have stretched so counting links will not translate to an exact fit for your new chain.  Your new chain will be slightly shorter and will require some re-adjustments to your rear deraileur.

Additionally, there's a few other variables that you can check/think about.

1.) New chains come with a protective grease/oil that protects the chain from cororosion.  There's some debate on whether you remove this coating and add chain lube or just keep it on.  I've always removed it since the viscosity is higher than my chain lube.  The viscosity of the lubricant you use will affect power transfer enough for you to notice.

2.) You may not get smooth shifting at all if your cassette is worn out with your new chain.  If this is the case the reason is that your old chain has worn into the cassette teeth - meaning the two fit together "perfectly".  When you replace the chain, the chain no longer sits properly within the teeth.  If you look at the cassette teeth and you see that they are shaped like shark teeth it's time to think about a replacement.