Same difference as a 4 lane highway vs an 8 lane highway in rush hour traffic.
Deeper explanation:
CPUs process information in series of 0s or 1s called bits.
a 1 Ghz computer process 1 Giga(billion) bits per second (hz)
An i5 has hyperthreading which means for every physical core, it can perform work for two threads. A thread is a pattern of 0s or 1s. A lane of the highway if you will.
Since the i5 is typically dual-core it has 2 physical processing cores, each which can perform work for two threads. So you can work on 4 threads at any given time.
An i7 also has hyperthreading but usually ships with a faster clock speed (2 Ghz for this example) and in the most common quad-core design it can perform work on 4 physical processing cores that each perform work on two threads or a total of 8 threads at a time.
So lets just say you have a dual-core i5 running at 1 Ghz and a quad-core i7 running at 1 Ghz, do the math and it turns out to be 4 Billion bits per second in the i5 (4 lanes of traffic) and 8 Billion bits per second in the i7 (8 lanes of traffic)
The only way they'd be close to equivalent is if you had a dual core i5 at 2 Ghz and an i7 at 1 Ghz, but you'd still see better response out of the system with the i7 since the processor can open up some threads to process more background tasks.