Are these two expressions considered different? Because my birthday is at the end of the year, I always considered 今年几岁 to be age at the end of the year, whereas 现在 is age from the most recent previous birthday that you've celebrated. If someone asks 今年几岁, I'd explain that 今年 I'm x years old, but right now I'm x - 1 years old.
现在几岁 sounds really weird. People usually say 今年几岁 or just 几岁 to mean the age as of right now. Come to think of it, I think this might be because there's a different notation of age which increases every lunar new year.
Edit: as pointed out by the comments below, 现在几岁 doesn't sound really weird in general. It's definitely less common than 今年几岁, but maybe it sounding really weird to me is a dialect thing.
Traditionally, people's "age" in China does not increase at birthday, but at the beginning of the (lunar) year. See the Chinese Wikipedia page for 虚岁. So "现在几岁" and "今年几岁" are actually the same. There are still people who would like to use this counting method for ages. This is not used in official documents.
Nowadays, the most commonly used counting method is to increase the age at the person's birthday. However, I personally would still treat the two expression the same. It just shows that the people asking wants to know your age. These expressions are casual and can be answered casually, so the technical difference before and after the birthday is not important.