So my question is, is it reasonable to have lower download speeds on a lower spec computer?
Late, but the simple answer is "maybe".
In short, it comes down to how much resources your hardware has, and that's not necessarily down to 'fast' or 'slow' hardware, so much as system config too.
Run a Userbench benchmark and see what aspects of your system are slow (if any). High levels of background CPU will be a telling sign of your system resources being leeched from apps, programs etc. It might be that it'll come down to faster hardware, but it might come down to servicing the software running on said system and making it less bloaty.