Torrevieja obviously has more facilities and amenities as it's a large city with a population over 100,000 rising to over 500,000 in the summer (many Spanish from Madrid and other places own homes there which they visit in August). Many of the areas in Torrevieja are very British orientated especially to the south in Orihuela Costa. There are many areas attached with their own good and bad points. Shops, supermarkets, clubs, shopping centres are all in abundance. There is also a very good bus service. The centre is city living, it can be noisy like any other city.
Villamartin is much smaller but very close to the Orihuela Costa area. It attracts golfers all year round. The main Villamartin Plaza is the centre with bars, cafes, shops and so on. A bit of a hike to the supermarkets but plenty of smaller shops. Not far to the Zenia Boulevard shopping mall (about 4 or 5km).
Personally, I would pick somewhere on the outskirts of Torrevieja like La Mata, San Luis, La siesta and so on. I'm not a fan of Villamartin and the Plaza can attract the worst of the British holidaymaker in the summer as can the Orihuela Costa. They are totally different off season but Villamartin attracts golfers all year round. I also wouldn't pick Torrevieja centre due to the noise, dog mess, graffiti (although the council is trying to do something about it).
We have lived on the outskirts of Villamartin, in a Torrevieja urb in between Orihuela Costa and Torrevieja before moving to our present location. We love it here but it has its drawbacks. Poor public transport and, again, gets extremely busy in the summer. Villamartin has a bus that goes to the beaches but nowhere else.
I think Villamartin comes under Orihuela Costa town hall, possibly the worst in the area. Virtually everything like trafico, residency etc are done in Elche or Orihuela as neither place has a National police presence.
Best thing is to visit and travel around looking at the areas. Guardamar is nice, lots of little towns around and property, though low in price, vary greatly in build quality. Our place in Villamartin was obviously built by the lowest tenders with poor quality plugs and switches, poor quality windows and doors, no earth connections to plumbing and really cold in winter. Our place in Torrevieja was a little better but our house now puts them all in the shade with excellent quality in comparison.