I bought a Squier Vintage Modified Jaguar (P/J), changed the PUPs, bridge and tuners, and I now have a bass that plays and sounds like a £750 bass but which in total cost me under £450. To my mind it also has the best of both Precision and Jazz basses tone-wise but on a very lightweight and small-bodied bass. In short, it's a bass that suits me perfectly but which I'd not be able to buy off the peg. I'd say that if you have an instrument that is half decent to start with - which is VERY important - and you know both what you want from a bass and what you're doing in terms of equipment selection, modding a cheap bass can be a very economic route to getting a decent bespoke instrument.
Good luck, and enjoy it!