For the first week, at least. Then they start to accumulate cruft and slow down, eventually becoming barely usable.
I've experienced it in the past. I see it happen for my friends and family. I decided some time ago to save up that $750 - $1k and go for the high-range phones, so that I can use them for two or three years without daily frustrations.
The top-most commenter is right. Phones are used even more frequently than cars; for many, even more frequently than other types of computers combined. It's one of those things it's not worth to cheap out on - like a mattress or an office chair.
(Now, of course part of me is happy for the mid-range phones costing what they do, because this is why high-end phones cost $1k and not $10k.)