Am framing my basement with metal studs.
There are no laod bearing considerations.
Is there a problem if I use 2 x 3 metal studs instead of 2x4.

If it isn't structural, I don't think it matters. In my area basements are framed with 2x3 wood studs all the time, as long as they aren't load bearing. But if it is perimiter walls, you might want to consider the matter more importantly if you are insulating. I've found it harder to find 2x3 insulation at places like Home Depot. But maybe my luck isn't good...

GeorgeM - Unless you want to buy special doors & windows . You need to go with reg. size 2x4s Good LUCK ::::: F.B.E.

Metal studs that I've used are standard size and with 1/2 sheetrock it will make a 4 and 1/2 jamb which is standard

I would not worry too much about the insulation since your framing will not be tight with the wall. Basement foundation walls get a bit wavy so I set my floor plate 1" away from the wall and then raise my wall sections in place. I would advise installing a 6mil visqueen vapor barrier directly to the wall and then use unfaced insulation or rigid foam panels. I also use paperless drywall. Mildew grows on drywall paper, not the gypsum.

My sister bought an 18 by 24 foot townhouse with a basement finished in 2X4s, what a waste of space. I'd be inclined to use only the framing needed to clear pipes and wiring. On flat, plumb walls, you can even glue&screw foam insulation to the concrete, then glue mold-resistant drywall to that. If you absolutely need 4" of insulation, you can also put 2X3s an inch away from the concrete; 2X4s would just conduct more heat and short-circuit the insulation anyway.