Should I consider buying a velomobile as my daily commute vehicle instead of a bike? What are the advantages/disadvantages between a (possibly electric) velomobile and a regular bike when in daily use?
By velomobile you mean something like this, a fully enclosed/faired bicycle, tricycle, or quadricycle:



Unless your commute is in the heavy rain/snow and you have a fully enclosed velo; or you're commuting more than 100 km on salt flats each way and need the air-resistance efficiency, there are very few advantages to a velomobile and very many disadvantages:

Velomobiles:


Are very heavy/slow going up hills, or starting up from stop lights for that matter
Are terrible to park (take too much space)
Are terrible to secure (no easy place to put a U-lock)
Are terrible at maneuvering (around your workplace's parking lot, for example) because you can't really walk most velos by yourself 
You're too large to split lanes but also too slow to keep up with traffic so that cars will honk at you when you take up an entire lane. 
Can't easily be carried up stairs
Won't fit on a bike rack, back of a car, or in an elevator. This has implications for mixed mode commuting (bike+bus or train) as well as makes it difficult if you have a major problem at the side of the road and need to transport the velo back home, to work, or to a repair shop. 
Many enclosed ones can be very hot in the summer
Are expensive to buy, fragile, and expensive to fix/maintain (thx Rider_X)
And ... are just the right height to get squished by a truck or bus


Now, electric-assist velomobiles do have some advantages, but (as the podride homepage you initially linked to itself notes,) the four wheel version is in a legal gray zone as in some jurisdictions it might be considered an automobile rather than a bike or motorcycle. And if you are in a jurisdiction where the motor is limited to 250 watts, be prepared for a lot of hard work pedaling. 

Tl;dr If you want a small electric car, get a small electric car like a neighborhood electric vehicle (USA) or motorized quadricycle (EU) These have license plates and can be driven and parked on local roads without any concerns about legality. They also have headlights, tail lights, turn signals, and other safety equipment.