I think everyone goes through this dilemma! Especially when #2 comes along!

I swear by my Mother's Choice stroller / pram with reversable handle.
It is lightweight, compact yet holds so much when you are out and about. It is great for newborns with the reversable handle and steers super! Great for walking too - I found that I could reverse the handle if the sun was in baby's eyes.

Also great to add a skateboard to for a toddler.

I also have a Bertini Bidwell 4 wheel steer with a toddler seat. While these are FANTASTIC for walking the streets I wasn't too taken with them in a busy shoping centre. Really hard to get around the tight spaces of department stores and very heavy. But it served it purpose for a newborn and toddler. I still use it for walking around the neighbourhood to the pool / playgroup etc. And great for day trips to the zoo. Just not practical enough for every day use.

I also have an umbrella stroller for quick trips into the shops.

But really - the good old standard 4 wheel pram / stroller is the way to go IMHO.!