This is a question that pops into the vast majority of guitar and bass players at some point of their journey into music playing and making, and it's one that can make us reflect about the value we give to objects.
First let's try to put aside the romantic side of buying a guitar, let's be focused and objective (or at least try it for a while..)
Whatever the option you go with at the moment, the fact is that both options start with the same raw materials, wood and hardware, and at the end both options end with the same, a guitar or a bass. Both can end up being good or bad, the process does not determine the final quality. So why worry about the process at all?!
This question can be even more pertinent if both end results end up being of good quality and at the same price point. There is no right or wrong answer, but personalization, originality, ergonomics and perception of value will probably be the factors to account for in this dilemma.
Factories objective is to make the same object over and over again, within the pre-establish deviation margins. Luthiers are simply not bound to such restraints, and therefore can be wild and creative. If you are going to hand carve a neck, then it shouldn't be so hard to increase its thickness and reduce nut width if that's the musician's desire. Factories are not so light to adjust to such requirements. Personalization and original shapes are also easier for a luthier to carry on than a factory production line.
But perception of value can be a tricky one! For the perception of value we have to separate the factories by affordable brands vs high end brands, and Luthiers in the first years of their careers vs Luthiers with many years of experience.
The value of affordable guitars is that they are affordable! Such instruments will most likely not see any increase in their monetary value in 20 years. High end factory guitars and basses might not see an increase either, but if they are well preserved they probably won't lose much value either. If the luthier making the instruments is very sought after, his instruments are high-end with a price tag to match and you rarely see one for sale on the used market then there is a good chance that instrument might see an increase in the value in the long term. One luthier can only make x guitars in his career.
When it comes to starting luthier you just don't know if it will be of any value in the future, and the chances it decreases in value are probably high, no one knows him yet! But on the other hand this might be the perfect time for you to strike a good deal because the price has not yet increased due to low demand and the waiting list is probably short.
But now let's add a bit of romanticism and add emotional perception of value to the mix! The fact is if I could afford it I would only own handmade objects, the reason being that they are just made with care and passion (well, in most cases anyway!). If in today's world you decide to make handmade objects for a living then the major factor for that decision has to be the passion you have for that object.
Millions of bottles of dove cream shower are sold every day, but only a few dozens of handmade soap bars made out of olive oil from the coasts of France are sold every day. Both do their job but the handmade soap bar will have a unique fragrance and feel to it (and probably will not have a plastic bottle...)
Now there are two paths luthiers can take, make only their original designs or make instruments using the classic electric guitars and bass shapes. If they are making classic shapes then they should feel very unique so they could stand on their own and not be confused with the original brand.(at least that's my perspective).
So to give my answer to the original question, it's all up to you! Both are valid options, but I think that handmade instruments truly make sense over factory ones is when the Luthier channels all his skills, passion and unique vision into original designs that you find appealing and feel a connection with them.
My best advice: choose the one that inspires you the most.