^^^ No, you DO get better fuel economy if you're comparing (let's say auto-transmission) base Echo and Corolla pound-for-pound (pun-intended, you'll see why).
- First of all, the base Echo is not more expensive, unless there're some places or dealerships scams I don't know about.
- Yes it has less space, which is obvious and self-explanatory size-wise anyway, but can still sit 2 full-size adults in the back seat comfortably, if not more comfortable than the Corolla's backseats.
- It does have less HP, but it really doesn't need more HP (the keyword here for most of us who have the need for speed is WANT more HP, since we never really NEED more HP). It has more than adequate amount of HP (can take the car up to 180km/h or 100mph, which is more than enough), and good torque to go with (I can cruise around in 5th gear manual all day in city traffic without the car breaking a sweat, it WILL be obviously slow but will pickup speed if throttle is smashed to the floor). And keep in mind, you use what you need, and the fact is that more HP equals more fuel consumption, period.
- Last but not least, one of the main reasons why an Echo will always get better fuel economy compare to a Corolla is the issue of WEIGHT, which the Echo has less. Less weight means less power required to move the car to speed, which in turn saves more fuel than a heavier car. Another side-benefit is better handling. Just put the same driver (of good driving or racing skills) in each car (with same or similar tire and fuel qualities) for some laps on a track (with not too many long straights), and the Echo WILL pull a quicker lap time. It's just plain physics.
Now keep in mind, you should get a type of car based on your needs. If you have a family (a wife with 3 small children or 2 teenagers per say), it'd probably be best to get a Corolla. Plus you get a decent size trunk to haul "stuff." If you're single and need to drive to places frequently but won't want to worry too much about fuel-costs and other costs such as maintenance and such, the Echo hatchback will more than suit your needs. Trust me, it HAS plenty of room for 4 people, or enough room for just 1 passenger while hauling a 27" CRT television (WITH the box which is BIGGER than the TV itself) in the back with the rear seats folded down. Try doing that with an older gen Civic hatch (the EG6 gen for example) and I bet the box wouldn't even clear the hatch opening, which will require the TV to be taken out of the box.
To add to that, there's always a matter of PREFERENCE, which is irrational but equally justifiable nonetheless. If the Echo meets your needs but you still want a Corolla for whatever reasons, you might as well get the Corolla, plain and simple, since that's what you wanted.
I hope the above will MORE THAN answer your questions, and apologies for spewing out so many words without knowing it, but hopefully you get the idea in the most objective way possible (with a hint of bias of course, guess it's somewhat an unescapable flaw of being a human

)
Cheers,
EchoHoLiK