Refurbished iphone or new one?

Refurbished means it was sold then returned (for whatever reason), apple then fixes 'all' the issues they can find. Refurbished is supposed to mean 'almost brand new' but that's not always the case.

If your having all those problems with your phone now, I think its a save bet a refurbished would work better. Its a gamble though.

The Apple iPhones have a Gorilla Glass screen that is extremely hardy against abuse, but if a screen protector was not used on the phone it may have fine scratches that make the screen hard to read, or affect the touch screen application’s responsiveness. Look for a refurbished phone with a new or like new screen for the best overall performance and visibility. While refurbished iPhones are less expensive than their new counterparts, and can often be purchased and activated without signing a new contract, it is important to remember that they are used phones, and may have issues caused by their previous owner. Whether a buyer is shopping online or offline, there are several things he or she should consider and ask about before purchasing a refurbished phone.

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Personally, from what you have said, it seems that you have gotten a defective one. Although this does happen from time to time, it is still a better idea to return the defective iPhone for a brand new replacement one. I have never liked refurbished products for a number of reasons. For one, refurbished products are typically restored using 3rd party or Non-OEM Parts which makes the longevity of the device in the long run much shorter and could potentially develop further problems in the future. When you are buying a new one, you know it is made with all OEM Parts and if there is ever an issue apple is obligated to replace it within 365 days REGARDLESS of apple care. Just retain the sales slip.